Question

What is the net area between `f(x) = x+8` and the x-axis over `x in [2, 4 ]`?

Answer 1

`22`

Explanation:

Using the rule:

`intx^ndx=(x^(n+1))/(n+1)+C`

Find the antiderivative of the function:

`F(x)=int(x+8)dx=x^2/2+8x+C`

To find the area, evaluate the integral from `F(2)` to `F(4)`, which is equivalent to `F(4)-F(2)`.

`=[x^2/2+8x] _ 2 ^4 =(4^2/2+8(4))-(2^2/2+8(2))=22`