Question

Set up integrals (do not evaluate) for the areas of surfaces of revolution, o by rotating the given curve around x-axis and around y-axis, using integration variable for both cases - a total of four integrals. Equation of the curve: y=arctanx,0≤x≤1

Answer 1

The integral setup for rotating the curve y = arctan(x) around both the x-axis and y-axis.

Step-by-step explanation:

When rotating the curve y = arctan(x) around the x-axis, the integral setup would be ∫[from 0 to 1] 2πy √(1 + (dy/dx)²) dx, where dy/dx is the derivative of y with respect to x.

When rotating the curve around the y-axis, the integral setup would be ∫[from 0 to π/4] 2πx √(1 + (dx/dy)²) dy, where dx/dy is the derivative of x with respect to y.