First slide

Evaluation of definite integrals

Question

$\int_{0}^{1} x^{2} {(1 - x)}^{5} d x =$

Easy

A

$\frac{1}{186}$
B

$\frac{1}{168}$
C

$\frac{1}{196}$
D

$\frac{1}{176}$

Solution

$\int_{0}^{1} x^{2} {(1 - x)}^{5} d x = \int_{0}^{1} {(1 - x)}^{2} x^{5} d x$
$= \int_{0}^{1} (x^{5} + x^{7} - 2 x^{6}) d x$

$\begin{matrix} = {(\frac{x^{6}}{6} + \frac{x^{8}}{8} - 2 \frac{x^{7}}{7})}_{0}^{1} \\ = \frac{1}{168} \end{matrix}$

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