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Published byClarence Shon Parker Modified over 5 years ago

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AP Calculus Definite Integrals Review (sections 5.6-5.10)

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Quiz Topics Fundamental Theorem of Calculus (section 5.6) Nderiv and FnInt on calculator Definite integral properties (section 5.7) Area using integrals (section 5.8) Example: Region bounded by y = -x^2 + 5 and y = -2x + 2 Volumes of solids (section 5.9)

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Fundamental Theorem of Calculus

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Integral Properties If function values of f(x) are positive and the interval boundaries are increasing, the integral will be positive. If functional values of f(x) are negative (below x axis) and the interval boundaries are increasing, the integral will be negative. As a result, it is possible to have areas of positive and negative area “cancel,” resulting in an integral of 0.

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Odd/Even Integrals with Symmetric Limits

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Reversal of limits of integration: Integral of Constant Times Function: Integral of Sum:

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Sum of Integrals With Same Integrand (Also allows integral to be broken into more convenient parts)

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Use Common Sense!

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Use Common Sense: Not all Integrals Involve Calculus!

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Area Bounded By Curves

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Area bounded by curves: “Sideways” Functions on left and right instead of top and bottom. Make sure “strip” always extends from one function to another (Not one function back to itself)

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Integral Vs. Area Be able to write the INTEGRAL EXPRESSION for the area.

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Additional Topics

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