Question

use the fundamental theorem to find the area under f(x)=x^2 between x=1 and x=4.

how do i go about doing this? i know how to use my calculator, but it says to use the theorem so i'm not completely sure.

Answer 1

The indefinite integral of x^2 is x^3/3. Calculate the vlalue of that function at x = 4 and subtract the value at x= 1. The difference is called the definite integral and will be equal to the area under the y = x^2 curve (measured above the x axis).