First slide

Evaluation of definite integrals

Question

$\int_{0}^{5} x {(5 - x)}^{10} d x =$

Easy

A

$\frac{5^{12}}{132}$
B

$\frac{5^{10}}{132}$
C

$\frac{1}{132}$
D

$\frac{5}{132}$

Solution

$\int_{0}^{5} x {(5 - x)}^{10} d x = \int_{0}^{5} (5 - x) x^{10} d x$
$= {(5 \frac{x^{11}}{11} - \frac{x^{12}}{12})}_{0}^{5}$

$= \frac{5^{12}}{132}$

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