Can you help me find the area of the region under the graph of the function f on the interval [0, 8]? f(x) = 8x − x2.

Answer 1

∫[8x - x²]dx = 4x² - (1/3)x³ evaluated between 0 and 8, which is (4)(8²) - (1/3)(8³) = (4)(64) - 512/3 = 256 - 512/3 = 85 1/3

Answer 2

The area under the graph can be found by taking the integral

from 0 to 8 of (8x-x^2)dx Antiderivative of (8x-x^2) is 4x^2-(x^3)/3

4(8)^2-(8^3)/3-0=4*64-(512/3)=256/3