Math 16a worksheet 13 find the area of the region bounded

Question

MATH 16A WORKSHEET 13-

(1) Find the value of k such that 30e^{15x^3} + 1 is an anti-derivative of kx²e^{15x^3}.

(2) Evaluate: (a) ₁∫² (x + 3/x)dx

(b)  ₁∫²(e^2x - e^-2x) dx

(3) Find the area of the region bounded by the curve f(x) = x² - 4 and the x-axis.

(4) Suppose the function f(x) satisfies f'(x) = -2x + 3 for all x. Compute f(3) - f(1).

(5) Let S be the region bounded by the curves y = 3x + 2, y = 0, x = 0, and x = 4. Find the volume of the solid of revolution obtained by revolving S about the x-axis.