First slide

Evaluation of definite integrals

Question

$\int_{1 / π}^{2 / π} \frac{Sin (\frac{1}{x})}{x^{2}} d x =$

Easy

A

1
B

$-$ 1
C

$\frac{1}{3}$
D

$\frac{π}{2}$

Solution

$\int_{1 / π}^{2 / π} \frac{S i n (\frac{1}{x})}{x^{2}} d x put \frac{1}{x} = t$ $\Rightarrow \frac{- 1}{x^{2}} d x = d t$
$\begin{matrix} = \int_{π}^{π / 2} S i n t (- d t) \\ = {[C o s t]}_{π}^{π / 2} \\ = 1 \end{matrix}$

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