Mathematics - Definite Integration Question with Solution | TestHub

$$I={\int }_{-3\pi /2}^{-\pi /2}\left[(x+\pi {)}^3+{\cos }^2(x+3\pi )\right]dx$$ Put $\mathrm{x}+\pi =\mathrm{t}$ $$\begin{array}{rl}& I={\int }_{-\pi /2}^{\pi /2}\left[t^3+{\cos }^{2}t\right]dt=2{\int }_0^{\pi /2}{\cos }^{2}tdt\\ & ={\int }_0^{\pi /2}(1+\cos 2t)dt=\frac{\pi }{2}+0.\end{array}$$