Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Problem 1: Surface Area Calculation**
Find the exact area of the surface obtained by rotating the curve about the x-axis.
\[ y = \sqrt{4 - x}, \quad 1 \leq x \leq 4 \]
**Explanation:**
- The problem involves calculating the surface area of a solid of revolution.
- The curve described by the function \( y = \sqrt{4 - x} \) is rotated around the x-axis.
- The bounds for x are from 1 to 4.
This involves using the formula for the surface area of a solid of revolution:
\[
A = 2\pi \int_{a}^{b} y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx
\]
Where \( y = \sqrt{4-x} \) and the derivative \(\frac{dy}{dx}\) will need to be found to complete the calculation.](https://content.bartleby.com/qna-images/question/211be2ba-4ec6-4936-b07a-1ed177a8094e/d19fc9be-82b1-4380-934b-9392e10237c1/z2ogw6o_processed.jpeg)
Transcribed Image Text:**Problem 1: Surface Area Calculation**
Find the exact area of the surface obtained by rotating the curve about the x-axis.
\[ y = \sqrt{4 - x}, \quad 1 \leq x \leq 4 \]
**Explanation:**
- The problem involves calculating the surface area of a solid of revolution.
- The curve described by the function \( y = \sqrt{4 - x} \) is rotated around the x-axis.
- The bounds for x are from 1 to 4.
This involves using the formula for the surface area of a solid of revolution:
\[
A = 2\pi \int_{a}^{b} y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx
\]
Where \( y = \sqrt{4-x} \) and the derivative \(\frac{dy}{dx}\) will need to be found to complete the calculation.
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