Question

If ${\int }_0^{\frac{\pi }{2}}cos\left(x\right)dx=athen{\int }_0^{\pi }cos\left(x\right)dx$ is equal to -

• A. $2a$
• B. $a^2$
• C. $0$
• D. $a$

Answer 1

The correct option is C $0$

${\int }_0^{2a}f\left(x\right)dx=2{\int }_0^{a}f\left(x\right)dx,iff(2a-x)=f\left(x\right)and0iff(2a-x)=-f\left(x\right)$
$Let2a=\pi$
We know that $cos(\pi -x)=-cos\left(x\right)$
$So,{\int }_0^{\pi }cos\left(x\right)dx=0$