Question

If $u_{10}=\underset{0}{\overset{\pi /2}{\int }}{x}^{10}\sin xdx$, then the value of $u_{10}+90u_8$ 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)

$U_{10}={\left(-x^{10}\cos x\right)}_0^{\pi /2}+\underset{0}{\overset{\pi /2}{\int }}10x^9\cos xdx$
$=10{\left[x^9\sin x\right]}_0^{\pi /2}-10\times 9\underset{0}{\overset{\pi /2}{\int }}{x}^8\sin xdx$
$U_{10}+90U_8=\frac{10\cdot {\pi }^9}{2^9}$