Question

Find the area of the surface generated by revolving the curve x=(1/4)cos(4t), y=3(1/4)sin(4t) on 0≤t≤(π/4) about the x-axis. What is the integral used to find the area of the surface generated by revolving the curve?

Option 1: ∫[0, π/4] 3/4cos(4t)dt
Option 2: ∫[0, π/4] 3/4sin(4t)dt
Option 3: ∫[0, π/4] 3/4(1/4)cos(4t)dt
Option 4: ∫[0, π/4] 3/4(1/4)sin(4t)dt

Answer 1

The integral used to find the area of the surface generated by revolving the given curve about the x-axis is ∫[0, π/4] 3/4(1/4)sin(4t)dt.

Step-by-step explanation:

To find the area of the surface generated by revolving the curve x=(1/4)cos(4t), y=3(1/4)sin(4t) on 0≤t≤(π/4) about the x-axis, we can use the integral ∫[0, π/4] 3/4(1/4)sin(4t)dt. This option, ∫[0, π/4] 3/4(1/4)sin(4t)dt, represents the integral used to find the area of the surface generated by revolving the curve.