Explain the steps required to find the length of a curve x = g(y) between y=c and y=d.

Consider the following curves on the given intervals.  

b. Use a calculator or software to approximate the surface area.

y=tan x , for 0≤x≤π/4; about the x-axis 

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

y = (x²+2)^3/2 / 3 on [0, 1]

Equal integrals Without evaluating integrals, explain the following equalities. (Hint: Draw pictures.)

b. ∫²₀(25−(x²+1)²) dx = 2∫₁⁵ y√y−1 dy

Different axes of revolution Suppose R is the region bounded by y=f(x) and y=g(x) on the interval [a, b], where f(x)≥g(x).

b. How is this formula changed if x0>b?

3–6. Setting up arc length integrals Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curves on the given interval.

y = 2 cos 3x on [−π,π]

64–68. Shell method Use the shell method to find the volume of the following solids.

A hole of radius r≤R is drilled symmetrically along the axis of a bullet. The bullet is formed by revolving the parabola y = 6(1−x²/R²) about the y-axis, where 0≤x≤R.

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

x = y⁴/4 + 1/8y², for 1≤y≤2

Use the general slicing method to find the volume of the following solids.

The solid whose base is the region bounded by the semicircle y=√1−x^2 and the x-axis, and whose cross sections through the solid perpendicular to the x-axis are squares