Proof For Definate Intergral (1 Viewer)

Lukybear · Feb 28, 2010

For this proof, can i do it like this?

$\int_{0}^{a} f(x)dx = \int_{0}^{a} f(a-x)dx$
$\text{Let u=a-x }, du = -dx , x=a \ u=0, x=0 \ u=a\\ \int_{0}^{a}f(a-x) = \int_{a}^{0}f(u) -du(\text{Swapping Limits })\\ =-\int_{a}^{0}f(u) \\ =\int_{0}^{a}f(u) du =\int_{0}^{a}f(x) dx ( \text{since u is dummy variable})$

cutemouse · Feb 28, 2010

Yep. That works.

Proof For Definate Intergral (1 Viewer)

Lukybear

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cutemouse

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