Question

Find the area of the surface generated when the given curve is revolved about the x-axis. y= 2x+5 on [0,1] The area of the generated surface is square units. (Type an exact answer, using a as needed.)

Answer 1

The area of the surface generated when the curve y = 2x + 5 is revolved about the x-axis can be found by using the formula for the surface area of a solid of revolution, substituting the original function and its derivative, and finally simplifying and solving the integral.

Step-by-step explanation:

To find the surface area of the surface generated when the curve y = 2x + 5 is revolved about the x-axis from 0 to 1, we can use the formula for the surface area of a solid of revolution:

A = ∫from a to b of 2πy√(1 + (dy/dx)²)dx. The derivative of our function y, dy/dx = 2. We then substitute the original function and its derivative into the formula:

A = ∫from 0 to 1 of 2π(2x+5)√(1+4)dx

We now simplify and solve the integral to find the exact surface area.

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