Question

If integral from 0 to 1 of f (x) d x = 4 and integral from 0 to 1 of g (x) d x = - 3, then integral from 0 to 1 of [2 f (x) minus g (x) ]d x =?

Answer 1

Given:

Hence,

Splitting the integral,

`\begin{gathered} \int_0^12f(x)dx-\int_0^1g(x)dx=2\int_0^1f(x)dx-\int_0^1g(x)dx \\ \\ Substituting\text{ the given integrals,} \\ 2(4)-(-3)=8+3 \\ =11 \end{gathered}`

Therefore, the answer is 11