Find the volume of the solid obtained by rotating the

Question

1. Find the average value of f(x) = (4 - x)^{ex^2-8x} on [1, 4].

2. Determine the area to the left of h(y) = 2 + 4y - y² and to the right of the line x = -1.

3. Find the area bounded by:

(a) y = x² + 8, y = 3x², x = -3 and x = 4

(b) y = 1/(x+2), y = (x+2)², x = -(3/2), and x = 1

4. Find the volume of the solid obtained by rotating the region bounded by the given curves about the given axis.

(a) Rotate the region bounded by y = 1/x, y = 1/3 and x = ½ about the x-axis.

(b) Rotate the region bounded by y = 1/x, y = 1/3 and x = ½ about the y-axis.

(c) Rotate the region bounded by x = y² - 8y + 19 and x = 2y + 3 about the x-axis.