A volume is described as follows:
1. The base is the region bounded by y = 2 - (2/25)x^2 and y = 0.
2. Every cross-section parallel to the x-axis is a triangle whose height and base are equal.
Find the volume of this object.
Volume =
2. Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 about the x-axis.
V =
3. Find the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0, and x = 2 about the y-axis.
V =
4. Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x = 0, y = 1, x = y^(1/4), about the line y = 1.
5. Find the arc length of y = 4x - 1 on 0 ≤ x ≤ 4.
6. Find the arc length of y = 2x^2 - 3 on 0 ≤ x ≤ 2.
7. Find the surface area of revolution about the x-axis of y = 4x + 4 over the interval 0 ≤ x ≤ 2.
8. Find the surface area of revolution about the x-axis of y = 2sin(7x) over the interval 0 ≤ x ≤ π/7.