Matching Volume Integral Questions

Question

Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = tan^3(x), y= 1, and x = 0 about the line y = 1?

a) π ∫(tan^3(x))^2 dx evaluated from π/4 to 0

b) π ∫(1 - tan^3(x))^2 dx evaluated from π/4 to 0

c) π ∫tan^5(x) dx evaluated from π/4 to 0

d) π ∫tan^5(x) dx evaluated from 1 to 0

e) π ∫(1 - tan^3(x))^2 dx evaluated from 1 to 0

f) π ∫(tan^3(x))^2 dx evaluated from 1 to 0

Cylindrical Shells Method and Disks/Washers methods are both applicable in these scenarios.

Answer 1

tan³x = 1; tanx = 1 , x = π/4. By disk method volume v = π∫₀^π/4(1 - tan³x)²dx

Answer is b)