Question

Can someone answer this please

Answer 1

(a) 12

Explanation:

The integral over the reverse range is the opposite of the integral over the forward range. The integral over adjoining ranges is the integral over the whole range.

Application

`\displaystyle \int_(-1)^5{f(x)}\,dx=\int_(-1)^1{f(x)}\,dx+\int_(1)^5{f(x)}\,dx\\\\=\int_(-1)^1{f(x)}\,dx-\int_(5)^1{f(x)}\,dx=5-1=4`

Then 3 times the integral is ...

`\displaystyle 3\int_(-1)^5{f(x)}\,dx=3(4)=\boxed{12}`