Definite Integrals Review (sections 5.6-5.9)

AP CalculusDefinite Integrals Review(sections 5.6-5.10)Quiz TopicsFundamental Theorem of Calculus (section 5.6)Nderiv and FnInt on calculatorDefinite integral properties (section 5.7)Area using integrals (section 5.8)Example: Region bounded by y = -x^2 + 5 and y = -2x + 2Volumes of solids (section 5.9)Fundamental Theorem of Calculus

Integral PropertiesIf 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 tobe broken into more convenient parts)

Use Common Sense!Use Common Sense: Not all Integrals Involve Calculus!

Area Bounded By Curves

Area bounded by curves: SidewaysFunctions 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. AreaBe able to write the INTEGRAL EXPRESSION for the area.

Additional TopicsAdditional Topics