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Find the volume of revolution shown on the right by rotating the area shown on the left about the x-axis. Use the disk method. Round your answer to the nearest thousandth.

Find the volume of revolution shown on the right by rotating the area shown on the left about the x x -axis. Use the disk method.\newlineRound your answer to the nearest thousandth.

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Full solution

Q. Find the volume of revolution shown on the right by rotating the area shown on the left about the x x -axis. Use the disk method.\newlineRound your answer to the nearest thousandth.
  1. Identify Function: Identify the function that bounds the area to be rotated. Let's say the function is f(x)f(x).
  2. Set Up Integral: Set up the integral for the volume using the disk method: V=π∫ab(f(x))2 dxV = \pi\int_{a}^{b} (f(x))^2 \, dx, where [a,b][a, b] is the interval of rotation.
  3. Calculate Integral: Calculate the integral to find the volume. This involves integrating the function f(x)2f(x)^2 from aa to bb and then multiplying by π\pi.
  4. Round Result: Round the result to the nearest thousandth as instructed.

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