2. Find the volume of rotation bounded by the region y = √(x), y = 0, and y = x - 2 when rotated

Name: 2. Find the volume of rotation bounded by the region y = √(x), y = 0, and y = x - 2 when rotated about the x-axis.
Uploaded: 2022-06-05T20:05:34-08:00
Duration: 2 min 37 s
Channel: Ryan Bradley
Description: 2. Find the volume of rotation bounded by the region y = √(x), y = 0, and y = x - 2 when rotated about the x-axis.

Step 1: First, we need to find the points of intersection of the curves. Setting $y = sqrt{x}$

Question

2. Find the volume of rotation bounded by the region $y = \sqrt{x}$, $y = 0$, and $y = x - 2$ when rotated about the x-axis.

          2. Find the volume of rotation bounded by the region $y = \sqrt{x}$, $y = 0$, and $y = x - 2$ when rotated about the x-axis.

2. Find the volume of rotation bounded by the region y = √(x), y = 0, and y = x - 2 when rotated about the x-axis.

Added by Paula M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ryan Bradley

06/05/2022

Step 1

Setting $y = \sqrt{x}$ and $y = x - 2$ equal to each other, we get $\sqrt{x} = x - 2$. Squaring both sides, we get $x = x^2 - 4x + 4$, which simplifies to $x^2 - 5x + 4 = 0$. Factoring, we get $(x - 1)(x - 4) = 0$, so $x = 1$ or $x = 4$. Since $y = \sqrt{x}$, Show more…

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