Problems

In Problems 1-130 find the derivatives by logarithmic differentiation.

In Problems 14-38 evaluate the integral.

39            Find the length of the parabola y = x², -1 ≤ x ≤ 1.

40            Find the surface area generated by rotating the parabola y = x², 0 ≤ x ≤ 1 about the x-axis.

41             Find the length of the spiral of Archimedes r = θ, 0 ≤ θ ≤ a, in polar coordinates.

42            Find the volume of the solid generated by rotating the region under the curve y = sec² x, 0 ≤ x ≤ π/3, about (a) the x-axis, (b) the y-axis.