Draw the graphs of y= 8cos(x) , y = sec^2(x) on the interval [-π/2, π/2]. Answer parts ABC below.

Question

Draw the graphs of y= 8cos(x) , y = sec^2(x) on the interval [-π/2, π/2]. Answer parts ABC below.

A). What are the points of intersection?

B). The enclosed region is rotated around the line x = π/2. Draw a picture of this graph

C). Find the volume of the solid

If possible please explain the step by step process in a video.

Answer 1

A). 8cosx = 1/cos²x; cos³x = 1/8; cosx = 1/2; x = ±π/3; y = 4; (- π/3, 4) and (π/3, 4)

B). You can graph using TI84

C). v = 2π∫_-π/3^π/3(π/2 - x)(8cosx - 1/cos²x)dx = 2π[(π/2 - x)(8sinx - tanx)_-π/3^π/3 + ∫_-π/3^π/3(8sinx - tanx)dx] =

2π[π/6(4√3 - √3) - 5π/6(- 4√3 + √3)] = 6√3π² = 102.568