Question

If $\underset{0}{\overset{a}{\int }}f\left(2a-x\right)dx=m$ and $\underset{0}{\overset{a}{\int }}f\left(x\right)dx=n,$ then $\underset{0}{\overset{2a}{\int }}f\left(x\right)dx$ is equal to

• A. 2m + n
• B. m + 2n
• C. m - n
• D. m + n

Answer 1

Answer: (D)

Put $x=2a-t$
so that $dx=-dt$
when $x=a,t=a$ and when $x=2a,t=0$
$\underset{0}{\overset{2}{\int }}f(x)dx=\underset{0}{\overset{a}{\int }}f(x)dx+\underset{0}{\overset{a}{\int }}f(2a-t)dt=n+m$