AP Calculus Definite Integrals Review (sections 5.6-5.10)

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Presentation transcript:

AP Calculus Definite Integrals Review (sections )

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)

Fundamental Theorem of Calculus

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.

Odd/Even Integrals with Symmetric Limits

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

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

Use Common Sense!

Use Common Sense: Not all Integrals Involve Calculus!

Area Bounded By Curves

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)

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

Additional Topics