Question

If integral from 1 to 5 of f(x)dx=20, find integral from 5 to 1 of (f(x)-2)dx?

Answer 1

`int_5^1 f(x)-2 \ dx = -12`

Explanation:

We are given that:

`I_1 = int_1^5 \ f(x) \ dx = 20`

Then we seek:

`I = int_5^1 f(x)-2 \ dx`
`\ \ = - \ int_1^5 f(x)-2 \ dx`
`\ \ = int_1^5 \ 2- f(x) \ dx`
`\ \ = int_1^5 \ 2 \ dx - int_1^5 \ f(x) \ dx`
`\ \ = [2x]_1^5 - I_1`
`\ \ = 2(5-1) - 20`
`\ \ = -12`