Question

For each of the surfaces, calculate its exact area.

b) The area bounded by the curves y = 4sqrt(x), y = 2x+2 and the x-axis. Use vertical rectangles.
c) Same curves but use horizontal rectangles.

Wouldn't using rectangles count as a approximate Riemann sum? Since they ask the exact area I was going to integrate the higher curve - the lower curve in the [0,1] bounds. I don't see how using vertical or horizontal rectangles is going to give me an exact fraction answer.

Thank you

Answer 1

for c) rectangles, you won't get exact area no matter how you do it, unless the width of the rectangles approaches zero.