Question

Find the area of the surface generated by revolving the curve x(t) = t - sin(t) and y(t) = 3 + cos(t) with t in [0, 2π], about the line y = 4. (You shall derive the correct definite

Answer 1

To find the area of the surface generated by revolving the curve, we can use the formula for the surface area of revolution.

Step-by-step explanation:

To find the area of the surface generated by revolving the curve, we can use the formula for the surface area of revolution. The formula is given by:

S = 2π∫[a,b] y(t) √[1 + (dx/dt)²] dt

In this case, the curve is given by x(t) = t - sin(t) and y(t) = 3 + cos(t). We need to find the values of a and b, which correspond to the limits of t in the interval [0, 2π].

Once we have the values of a and b, we can evaluate the integral to find the area of the surface generated by revolving the curve.