Final answer:
To find the surface area of revolution about the x-axis of y=3sin(5x) over the interval 0≤x≤π/5, we can use the formula for surface area of revolution and evaluate the integral.
Step-by-step explanation:
To find the surface area of revolution about the x-axis of y=3sin(5x) over the interval 0≤x≤π/5, we can use the formula for surface area of revolution:
SA = ∫2πy√(1+(dy/dx)²)dx
First, we find the derivative of y with respect to x: dy/dx = 3cos(5x).
Then, we substitute the given values into the formula and integrate from 0 to π/5:
SA = ∫[0,π/5] 2π(3sin(5x))√(1+(3cos(5x))²)dx
After evaluating the integral, we can find the surface area of revolution about the x-axis.