Mathematics - Definite Integration Question with Solution | TestHub

$f\left(2-x\right)=f\left(2+x\right)$and$f\left(4-x\right)=f(4+x)$

Then curve is symmetric about$x=2$and$x=4$

$\therefore$The curve is periodic with period$4$

Given$\underset{0}{\overset{2}{\int }}f\left(x\right)dx=5$

$\underset{0}{\overset{4}{\int }}f\left(x\right)dx=2\underset{0}{\overset{2}{\int }}f\left(x\right)dx=10$

$\underset{10}{\overset{50}{\int }}f\left(x\right)dx=\underset{2\left(4\right)+2}{\overset{12\left(4\right)+2}{\int }}f\left(x\right)dx$

$=\left(12-2\right)\underset{0}{\overset{4}{\int }}f\left(x\right)dx$

$=10\times 10=100$