Question

If $u_{10}=\int\limits_0^{\pi / 2} x^{10} \sin x d x$, then the value of $u_{10}+90 u_8$ is :

• A. $9\left(\frac{\pi}{2}\right)^8$
• B. $\left(\frac{\pi}{2}\right)^9$
• C. $10\left(\frac{\pi}{2}\right)^9$
• D. $9\left(\frac{\pi}{2}\right)^9$

Answer 1

Answer: (C)

$U_{10}=\left(-x^{10} \cos x\right)_0^{\pi / 2}+\int\limits_0^{\pi / 2} 10 x^9 \cos x d x$
$=10\left[x^9 \sin x\right]_0^{\pi / 2}-10 \times 9 \int\limits_0^{\pi / 2} x^8 \sin x d x$
$U_{10}+90 U_8=\frac{10 \cdot \pi^9}{2^9}$