Question

Solve this:-

$f\left(x\right)=\int sin\frac{\pi }{2}(x+1),x\le 0$

Answer 1

We have,

$f\left(x\right)=\int \sin \frac{\pi }{2}(x+1)dx,x\le 0$

$f\left(x\right)=\int 1.(x+1)dx[\sin \frac{\pi }{2}=1]$

$=\int (x+1)dx$

$=\int xdx+\int 1dx$

$\text{On Integrate and we get}$

$=\frac{x^2}{2}+x+C$

Hence, this is the answer.