Aspire Faculty ID #15200 · Topic: JAMIA MCA 2017 · Just now
JAMIA MCA 2017

\(\displaystyle \int_{0}^{1}\frac{x}{(1-x)^{3/4}}\,dx\) is equal to …

Solution

Let \(u=1-x\Rightarrow du=-dx\). Then \[ \int_{0}^{1}\frac{x}{(1-x)^{3/4}}dx =\int_{1}^{0}\frac{1-u}{u^{3/4}}(-du) =\int_{0}^{1}\left(u^{-3/4}-u^{1/4}\right)du = \left[4u^{1/4}-\frac{4}{5}u^{5/4}\right]_{0}^{1} =4-\frac{4}{5}=\frac{16}{5}. \] \(\boxed{\tfrac{16}{5}}\)

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