Math 152 Quiz 1

Math 152 Quiz 1
Compute the following integrals:
1. Find the area between the curve y = x3 and the tangent line to this curve
at (2, 8). Yes, the tangent line does meet the curve in two points, and
both points have x-coordinates that are multiples of 2.
2. Let r be the distance between the center of a regular polygon and one of
its vertices, and let n be the number of sides. Then the area is given by
nr 2
2 sin n . Fix a base radius r, a height h, and the number of sides n.
Find the volume of a pyramid with base given by a regular n-gon with
radius r and height h. Hint: Set it up as an integral.