Question

What is the net area between `f(x) = x^3+6/x` and the x-axis over `x in [2, 4 ]`?

Answer 1

64.1589

Explanation:

Integrate `f(x)` over the region setting 2 as the lower limit and 4 as the upper limit.

`Area = int_2^4f(x)dx`
`= int_2^4 x^3+6/xdx = [x^4/4+6lnAbs(x)]_2^4`
`= {(4)^4/4+6ln(4)}-{(2)^4/4+6ln(2)}`
`=64+12ln(2)-4-6ln(2)`

`=60+6ln(2) approx 64.1589`