Question

${\int }_0^{10}\frac{x^{10}}{(10-x{)}^{10}+x^{10}}dx$ is equal to :

• A. $10$
• B. $5$
• C. $2$
• D. $\frac{1}{2}$
• E. $0$

Answer 1

Answer: (B)

$5$

Let $I={\int }_0^{10}\frac{x^{10}}{(10-x{)}^{10}+x^{10}}dx$ .....(i)
$\Rightarrow I={\int }_0^{10}\frac{(10-x{)}^{10}}{(10-x{)}^{10}+x^{10}}$ .....(ii)
On adding equations (i) and (ii), we get
$2I={\int }_0^{10}1dx=[x{]}_0^{10}$
$\Rightarrow 2I=10$

$\Rightarrow I=5$