The surface area A of a solid of revolution is given by the formula:

A = 2π ∫[a,b] f(x) * sqrt(1 + (f'(x))^2) dx

where f(x) is the function defining the curve, [a,b] is the interval over which to integrate, and f'(x) is the derivative of f(x).

In this case, f(x) = x^2, so f'(x) = 2x.

Substituting these into the formula gives:

A = 2π ∫[0,1] x^2 * sqrt(1 + (2x)^2) dx

This integral is a bit tricky to solve by hand, but you can use a calculator or software to get the numerical answer.

Question

The surface area A of a solid of revolution is given by the formula:

A = 2π ∫[a,b] f(x) * sqrt(1 + (f'(x))^2) dx

where f(x) is the function defining the curve, [a,b] is the interval over which to integrate, and f'(x) is the derivative of f(x).

In this case, f(x) = x^2, so f'(x) = 2x.

Substituting these into the formula gives:

A = 2π ∫[0,1] x^2 * sqrt(1 + (2x)^2) dx

This integral is a bit tricky to solve by hand, but you can use a calculator or software to get the numerical answer.

Knowee AI · Accepted Answer

The surface area A of a solid of revolution is given by the formula:

A = 2π ∫[a,b] f(x) * sqrt(1 + (f'(x))^2) dx

where f(x) is the function defining the curve, [a,b] is the interval over which to integrate, and f'(x) is the derivative of f(x).

In this case, f(x) = x^2, so f'(x) = 2x.

Substituting these into the formula gives:

A = 2π ∫[0,1] x^2 * sqrt(1 + (2x)^2) dx

This integral is a bit tricky to solve by hand, but you can use a calculator or software to get the numerical answer.

Find the surface area of a surface created by rotating the region bounded by 𝑓(𝑥) = 𝑥2 and the x-axis, on [0,1], about the x-axis