Question

$\stackrel{-\pi /2}{\underset{-3\pi /2}{\int }}\left\{\right(x+\pi {)}^3\}dx=$

• A. $\frac{\pi }{2}$
• B. $\frac{5{\pi }^4}{8}$
• C. $\frac{5{\pi }^4}{16}$
• D. none of these

Answer 1

Answer: (B)

$\frac{5{\pi }^4}{8}$

Now,

$\stackrel{-\pi /2}{\underset{-3\pi /2}{\int }}\left\{\right(x+\pi {)}^3\}dx$

$=\stackrel{-\pi /2}{\underset{-3\pi /2}{\int }}\left\{\right(-\pi -x+\pi {)}^3\}dx$ [ Using property of definite integral]

$=-\stackrel{-\pi /2}{\underset{-3\pi /2}{\int }}{x}^{3}dx$

$=-{\left[\frac{x^4}{4}\right]}_{-\frac{3\pi }{2}}^{-\frac{\pi }{2}}$

$=\frac{1}{4}\frac{3^4-1}{2^4}\times {\pi }^4$

$=\frac{5{\pi }^4}{8}$