Set up integrals to find the volumes of the solids formed by revolving the region bounded by the graphs of y = 16 – x² and y = 0 about the following lines: y = -5: Volume is dx where a = and b = y = 32: Volume is dx where a = and b = x = 8: Volume is dy where a = H and b =
Set up integrals to find the volumes of the solids formed by revolving the region bounded by the graphs of y = 16 – x² and y = 0 about the following lines: y = -5: Volume is dx where a = and b = y = 32: Volume is dx where a = and b = x = 8: Volume is dy where a = H and b =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Set up integrals to find the volumes of the solids formed by revolving the region bounded by the graphs of \( y = 16 - x^2 \) and \( y = 0 \) about the following lines:**
1. **Line \( y = -5 \):**
\[
\text{Volume is } \int_{a}^{b} \; \; \; dx \text{ where } a = \; \; \; \text{ and } b = \; \; \; .
\]
2. **Line \( y = 32 \):**
\[
\text{Volume is } \int_{a}^{b} \; \; \; dx \text{ where } a = \; \; \; \text{ and } b = \; \; \; .
\]
3. **Line \( x = 8 \):**
\[
\text{Volume is } \int_{a}^{b} \; \; \; dy \text{ where } a = \; \; \; \text{ and } b = \; \; \; .
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03b23b5b-7403-4fea-9f0d-7375440b9260%2F22efd0b9-7bf6-49c3-9f4b-a554139f7073%2Fldc0ar_processed.png&w=3840&q=75)
Transcribed Image Text:**Set up integrals to find the volumes of the solids formed by revolving the region bounded by the graphs of \( y = 16 - x^2 \) and \( y = 0 \) about the following lines:**
1. **Line \( y = -5 \):**
\[
\text{Volume is } \int_{a}^{b} \; \; \; dx \text{ where } a = \; \; \; \text{ and } b = \; \; \; .
\]
2. **Line \( y = 32 \):**
\[
\text{Volume is } \int_{a}^{b} \; \; \; dx \text{ where } a = \; \; \; \text{ and } b = \; \; \; .
\]
3. **Line \( x = 8 \):**
\[
\text{Volume is } \int_{a}^{b} \; \; \; dy \text{ where } a = \; \; \; \text{ and } b = \; \; \; .
\]
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