Question

${\int }_0^{\infty }\frac{x^{2}dx}{(1+x^2{)}^{7/2}}=$

• A. 1/15
• B. 2/15
• C. -1/15
• D. $\frac{4}{15}$

Answer 1

Answer: (B)

2/15

$x=tan\theta$
${\int }_0^{\frac{\pi }{2}}\frac{ta{n}^2\theta }{se{c}^7\theta }se{c}^2\theta \cdot d\theta$
$={\int }_0^{\frac{\pi }{2}}si{n}^2\theta co{s}^3\theta d\theta$
$={\int }_0^{\frac{\pi }{2}}(1-co{s}^2\theta )co{s}^3\theta d\theta$
${\int }_0^{\frac{\pi }{2}}co{s}^3\theta d\theta -{\int }_0^{\frac{\pi }{2}}co{s}^5\theta d\theta$
$=\left[\frac{2}{3}\right]-[\frac{4}{5}\times \frac{2}{3}]$
$=\frac{2}{3}\left(\frac{1}{5}\right)=\frac{2}{15}$