Question

What is the net area between `f(x) = 3x^2-4x+2` and the x-axis over `x in [1, 3 ]`?

Answer 1

`int_1^3 (3x^2-4x+2) dx=14`

Explanation:

To work this out, we need to evaluate the definite integral between 3 and 1.

Area=`int_1^3 (3x^2-4x+2) dx`
`=[3(x^3/3)-4(x^2/2)+2x]_1^3`
`=[x^3-2x^2+2x]_1^3`
`=[(3)^3-2(3)^2+2(3)]-[(1)^3-2(1)^2+2(1)]`
`=15-1`
`=14`