Integral Calculus


Calculus II


Calculus II deals with integration of functions. Introduces the Fundamental Theorem of Calculus


Calculus I


The main textbook used today is Stewart Calculus 8th edition. The relevant chapters are 5-8 and 11


[expand title=”6. Applications of Integration” rel=”submenu-highlander”]

[expandsub2 title=”6.1-Areas Between Curves” rel=”submenu-highlander1″]

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[expandsub4 title=”Finding Areas Between Curves” rel=”submenu-highlander2″]

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[expandsub4 title=”Area Between Curves – Integrating with Respect to y” rel=”submenu-highlander2″]

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[expandsub4 title=”Area Between Curves – Integrating with Respect to y – Part 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”6.2-Volumes” rel=”submenu-highlander1″]

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[expandsub2 title=”6.3-Volumes by Cylindrical Shells” rel=”submenu-highlander1″]

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[expandsub4 title=”Longer Version – Volumes using Disks/Washers” rel=”submenu-highlander2″]

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[expandsub4 title=”Volumes of Revolution – Disk/Washers Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Volumes of Revolution – Disk/Washers Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Volumes of Revolution – Disk/Washers Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Volumes of Revolution about Vertical Lines Using Washers” rel=”submenu-highlander2″]

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[expandsub4 title=”Longer Version – Volumes using Cylindrical Shells” rel=”submenu-highlander2″]

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[expandsub4 title=”Volumes of Revolution – Cylindrical Shells” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”6.4-Work” rel=”submenu-highlander1″]

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[expandsub4 title=”Work and Hooke’s Law – Ex 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Work and Hooke’s Law – Ex 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Calculating the Work Required to Drain a Tank” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”6.5-Average Value of a Function” rel=”submenu-highlander1″]

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[expandsub4 title=”The Mean Value Theorem” rel=”submenu-highlander2″]

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[expandsub4 title=”Average Value of a Function on an Interval Using Calculus” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expand title=”7.-Techniques of Integration” rel=”submenu-highlander”]

[expandsub2 title=”7.1-Integration by Parts” rel=”submenu-highlander1″]

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[expandsub4 title=”Deriving the Integration by Parts Formula – Easy!” rel=”submenu-highlander2″]

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[expandsub4 title=”Integration by Parts – Definite Integral” rel=”submenu-highlander2″]

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[expandsub4 title=”Integration By Parts – Using IBP’s Twice” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”7.2-Trigonometric Integrals” rel=”submenu-highlander1″]

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[expandsub4 title=”Trigonometric Integrals – Part 1 of 6″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Integrals – Part 2 of 6″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Integrals – Part 3 of 6″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Integrals – Part 4 of 6″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Integrals – Part 5 of 6″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Integrals – Part 6 of 6″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”7.3-Trigonometric Substitution” rel=”submenu-highlander1″]

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[expandsub4 title=”Trigonometric Substitution – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Substitution Example 1 Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Substitution Example 1 Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Substitution – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Substitution – Example 3 / Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Substitution – Example 3 / Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Trigonometric Substitution, Ex 4 – Rational Powers” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”7.4-Integration of Rational Functions by Partial Fractions” rel=”submenu-highlander1″]

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[expandsub4 title=”Partial Fraction Decompositions and Long Division” rel=”submenu-highlander2″]

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[expandsub4 title=”Integration Using Partial Fractions / Rationalizing Sub” rel=”submenu-highlander2″]

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[expandsub4 title=”A Complete Partial Fractions Problem” rel=”submenu-highlander2″]

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[expandsub4 title=”Long Partial Fractions Problem – Repeated Irreducible Quadratic Factors, Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Long Partial Fractions Problem – Repeated Irreducible Quadratic Factors, Part 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”7.5-Strategy for Integration” rel=”submenu-highlander1″]

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[expandsub4 title=”What Integration Technique Do I Use? Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”What Integration Technique Do I Use ? Example 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”7.6-Approximate Integration” rel=”submenu-highlander1″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”7.8-Improper Integrals” rel=”submenu-highlander1″]

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[expandsub4 title=”Improper Integral – Basic Idea and Example ” rel=”submenu-highlander2″]

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[expandsub4 title=”Improper Integral with Infinite Discontinuity at Endpoint” rel=”submenu-highlander2″]

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[expandsub4 title=”Improper Integral – Infinity in Upper and Lower Limits” rel=”submenu-highlander2″]

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[expandsub4 title=”Improper Integral w/ Infinite Discontinuity in the Middle” rel=”submenu-highlander2″]

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[expandsub4 title=”Improper Integral – More Complicated Example” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expand title=”8.-Further Applications of Integration” rel=”submenu-highlander”]

[expandsub2 title=”8.1-Arc Length” rel=”submenu-highlander1″]

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[expandsub4 title=”Arc Length” rel=”submenu-highlander2″]

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[expandsub4 title=”Arc Length Using Parametric Curves” rel=”submenu-highlander2″]

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[expandsub4 title=”Arc Length Using Parametric Curves – Example 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”8.2-Area of a Surface of Revolution” rel=”submenu-highlander1″]

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[expandsub4 title=”Finding Surface Area – Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Surface Area – Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Parametric Curves – Calculating Area” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”8.3-Applications to Physics and Engineering” rel=”submenu-highlander1″]

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[expandsub2 title=”8.4-Applications to Economics and Biology” rel=”submenu-highlander1″]

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[expandsub2 title=”8.5-Probability” rel=”submenu-highlander1″]

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[expand title=”11.-Infinite Sequences and Series” rel=”submenu-highlander”]

[expandsub2 title=”11.1-Sequences” rel=”submenu-highlander1″]

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[expandsub4 title=”Summation Notation” rel=”submenu-highlander2″]

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[expandsub4 title=”Sequences – Examples showing convergence or divergence” rel=”submenu-highlander2″]

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[expandsub2 title=”11.2-Series” rel=”submenu-highlander1″]

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[expandsub4 title=”What is a Series” rel=”submenu-highlander2″]

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[expandsub4 title=”Geometric Series and the Test for Divergence – Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Geometric Series and the Test for Divergence – Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Geometric Series – Expressing a Decimal as a Rational Number” rel=”submenu-highlander2″]

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[expandsub4 title=”Telescoping Series Example” rel=”submenu-highlander2″]

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[expandsub4 title=”Showing a Series Diverges using Partial Sums” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”11.3-The Integral Test and Estimates of Sums” rel=”submenu-highlander1″]

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[expandsub4 title=”Using the Integral Test for Series” rel=”submenu-highlander2″]

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[expandsub4 title=”Remainder Estimate for the Integral Test” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”11.4-The Comparison Tests” rel=”submenu-highlander1″]

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[expandsub4 title=”Limit Comparison Test and Direct Comparison Test” rel=”submenu-highlander2″]

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[expandsub4 title=”Limit Comparison Test and Direct Comparison Test 2″ rel=”submenu-highlander2″]

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[expandsub2 title=”11.5-Alternating Series” rel=”submenu-highlander1″]

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[expandsub4 title=”Alternating Series” rel=”submenu-highlander2″]

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[expandsub4 title=”More Alternating Series Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Alternating Series Estimation Theorem” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”11.6-Absolute Convergence and the Ratio and Root Tests” rel=”submenu-highlander1″]

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[expandsub4 title=”Using the Ratio Test to Determine if a Series Converges #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Using the Ratio Test to Determine if a Series Converges #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Using the Ratio Test to Determine if a Series Converges #3 (Factorials)” rel=”submenu-highlander2″]

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[expandsub4 title=”Root Test for Series” rel=”submenu-highlander2″]

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[expandsub4 title=”Absolute Convergence, Conditional Convergence and Divergence” rel=”submenu-highlander2″]

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[expandsub2 title=”11.7-Strategy for Testing Series” rel=”submenu-highlander1″]

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[expandsub4 title=”Strategy for Testing Series – Series Practice Problems” rel=”submenu-highlander2″]

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[expandsub2 title=”11.8-Power Series” rel=”submenu-highlander1″]

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[expandsub4 title=”Radius of Convergence for a Power Series” rel=”submenu-highlander2″]

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[expandsub2 title=”11.9-Representations of Functions as Power Series” rel=”submenu-highlander1″]

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[expandsub4 title=”Differentiating and Integrating Power Series” rel=”submenu-highlander2″]

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[expandsub4 title=”Multiplication and Division of Power Series” rel=”submenu-highlander2″]

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[expandsub2 title=”11.10-Taylor and Maclaurin Series” rel=”submenu-highlander1″]

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[expandsub4 title=”Taylor and Maclaurin Series – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Taylor / Maclaurin Series for Sin (x)” rel=”submenu-highlander2″]

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[expandsub4 title=”Taylor and Maclaurin Series – Example 2″ rel=”submenu-highlander2″]

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[expandsub2 title=”11.11-Applications of Taylor Polynomials” rel=”submenu-highlander1″]

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