11 lines
403 B
Markdown
11 lines
403 B
Markdown
The integration by parts formula is:
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$$ \int udv = uv - \int vdu $$
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## Deriving the Integration by Parts Formula
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$$ \frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) $$
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1. Integrating both sides, we get:
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$$\int \frac{d}{dx} (f(x)g(x))dx = \int [f'(x)g(x) + f(x)]$$
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2. Through the distributive property of integrals,
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$$ = \int f'(x)g(x)dx + \int f(x)g'(x)dx $$
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3. Therefore:
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$$f(x)g(x) = \intf'(x)g(x)dx $$ |