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TAMU
MATH 152 -
Integration
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1 8.1: Integration by PartsRecall the Product Rule for Derivatives (use u, v du, and dv):d(uv) =Integrate both sides and solve for u dv:Thereforeˆu dv =This formula is the key to Integration by Parts. The key is to choose what part of the integral isto be u and what part is to be dv.Examples:ˆx cos x dx =1ˆ10x2e−2xdx =ˆx2ln x dx =2On Beyond Average:ˆe2xcos(3x) dx =ˆx5sin(x3− 1) dx =Suppose f(0) = 3, f(2) = 4, andˆ20x2f(x) dx = 5. What isˆ20x3f0(x)
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