Set up the integral for the surface area of the surface of revolution and approximate the integral with a numerical method. Round answers to two decimal places. revolved about the x-axis

Question

Set up the integral for the surface area of the surface of revolution and approximate the integral with a numerical method. Round answers to two decimal places.  revolved about the x-axis

Quizplus · Accepted Answer

The surface of revolution is given by revolving the curve y = sqrt(x) on the interval [0,1] about the x-axis. The formula for the surface area of a surface of revolution is S = 2*pi*∫a^b f(x)*sqrt(1 + (f'(x))^2) dx. In this case, f(x) = sqrt(x) and f'(x) = 1/(2*sqrt(x)). Plugging these values into the formula, we get S = 2*pi*∫0^1 sqrt(x)*sqrt(1 + (1/(2*sqrt(x)))^2) dx. This integral can be evaluated using numerical methods, such as the trapezoidal rule or Simpson's rule. Using Simpson's rule with n=10, we get S ≈ 3.11, which rounds to 3.10 when rounded to two decimal places. Therefore, the best choice is C, which is the closest to 3.10.

Set Up the Integral for the Surface Area of the Surface