Question

If f and g are functions such that Integral from 0 to 2 of f (x) d x = 2 and Integral from 0 to 2 of (f (x) minus 2 g (x)) d x = 8, what is the value of Integral from 0 to 2 of g (x) d x?

Answer 1

Find the integral of the function below:

`\int_0^2f(x)dx=2`

`\int_0^(\infty)(f(x)-2g(x))dx=8`

Resolve the integration as a continuous integral on [0 ,2]

`\int_0^2(f(x)-2g(x))dx=\int_0^2f(x)dx-\int_0^22g(x)dx`
`\begin{gathered} 2-\int_0^22g(x)dx=8 \\ -2\int_0^2g(x)dx=8-2 \\ -2\int_0^2g(x)dx=6 \\ \int_0^2g(x)dx=-3 \end{gathered}`

Therefore the correct answer = -3

Option B