Question 8.T.15: (Integration by Parts) Let f, g : [a, b] → R be differentiab...

Elements of Real Analysis

(Integration by Parts)

Let $f, g : [a, b] → \mathbb{R}$ be differentiable on [a, b]. If $f^{\prime} , g^{\prime} ∈ \mathcal{R}(a, b) ,$ then

$\int_{a}^{b}{f (x)g^{\prime}(x)dx} = f (b) g (b) − f (a) g (a) − \int_{a}^{b}{f^{\prime} (x)g(x)dx}.$ (8.20)

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