Question

The value of the integral ${\int }_0^{\pi }{\int }_y^{\pi }\frac{sinx}{x}dxdy$, is equal to

• A. 2

Answer 1

The correct option is A 2
$I={\int }_0^{\pi }{\int }_y^{\pi }\frac{sinx}{x}.dx.dy$


After changing the limits
$I={\int }_0^{\pi }{\int }_0^{\pi }\frac{sinx}{x}.dy.dx$
$I={\int }_0^{\pi }\frac{sinx}{x}(y{)}_0^x.dx$
$I={\int }_0^{\pi }\frac{sinx}{x}\left(x\right).dx$
$I={\int }_0^{\pi }sinx.dx$
$I=(-cosx{)}_0^{\pi }$
$I=(1-(-1\left)\right)$
$I=2$