Question
The value of $\int_{0}^{1} x^{3 / 2}(1-x)^{3 / 2} d x$ is(a) $\pi=32$(b) $-\pi / 32$$\begin{array}{ll}\text { (c) } 3 \pi / 128 & (d)-3 \pi / 128\end{array}$
Step 1
The integral \(\int_{0}^{1} x^{3/2}(1-x)^{3/2} dx\) resembles the Beta function, which is defined as: \[ B(p, q) = \int_{0}^{1} t^{p-1} (1-t)^{q-1} dt \] for \(p, q > 0\). Show more…
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