First slide

Evaluation of definite integrals

Question

$\int_{- 2}^{2} | xcos πx | dx$ is equal to

Moderate

A

$\frac{8}{π}$
B

$\frac{4}{π}$
C

$\frac{2}{π}$
D

$\frac{1}{π}$

Solution

Since , $I = \int_{- 2}^{2} | xcos πx | dx = 2 \int_{0}^{2} | xcos πx | dx$
$= 2 \{\int_{0}^{\frac{1}{2}} | xcos πx | dx + \int_{\frac{1}{2}}^{\frac{3}{2}} | xcos πx | dx + \int_{\frac{3}{2}}^{2} | xcos πx | dx\}$
$= \frac{8}{π}$

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