Question

${\int }_{\frac{-3\pi }{2}}^{-\frac{\pi }{2}}\left[\right(x+\pi {)}^3+co{s}^2(x+\pi )]dx$ is equal to

• A. $\left(\frac{{\pi }^4}{32}\right)+\left(\frac{\pi }{2}\right)$
• B. $\frac{\pi }{2}$
• C. $-1$
• D. $\frac{{\pi }^4}{32}$

Answer 1

The correct option is B $\frac{\pi }{2}$

Let $l={\int }_{\frac{-3\pi }{2}}^{-\frac{\pi }{2}}\left[\right(x+\pi {)}^3+co{s}^2(x+\pi )]dx$
$Putx+\pi =t$
$l={\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}[t^3+co{s}^{2}t]dt$
$\Rightarrow l={\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}co{s}^{2}tdt=\frac{\pi }{2}$