Calculus homework

Question

2) Find the Area of Region R bounded by f(x) = 2x ^ 2 x = 0 (y axis), x = 2 , and y = 0(x - axis)

Answer 1

integral of 2x^2 = 2x^3/3

evaluate at x=2

2(2)^3/3 = 16/3 = 5 1/3

You can check the answer by doing 2 simple rectangles

with midpoints 1/2 and 3/2. each with a base of 1

heights of 2(1/2)^2 and 2(3/2)^2

that 1 by 1/2 and 1 by 9/2, add them to get 10/2 = 5, which is close to the exact area: 5 1/3