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?

Question

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?
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Solution 1

To find the surface area of a surface created by rotating a curve around the x-axis, we can use the formula for the surface area of revolution:

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

Here, f(x) = x^2 is the function that defines the curve, and f'(x) = 2x is its derivative. The limits Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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