Use the shell method to write and evaluate the de y = 8 - x -1 6- YA 2- x 4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Use shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis
**Transcription for Educational Website:**

Title: Using the Shell Method to Evaluate Volumes

Instructions: Use the shell method to write and evaluate the definite integral.

Equation: \( y = 8 - x \)

Response: \(-1\) ❌

---

**Diagram Explanation:**

The graph displays a triangular region under the line \( y = 8 - x \) on the coordinate plane. The triangle is shaded in blue and bounded by the x-axis from \( x = 0 \) to \( x = 8 \), and the y-axis.

- The hypotenuse of the triangle is the graph of the equation \( y = 8 - x \), which intersects the x-axis at \( (8, 0) \) and the y-axis at \( (0, 8) \).
- There is a vertical yellow rectangle within the triangle at \( x = 4 \), representing a typical shell or element used in setting up the integral for the shell method.
- The x-axis and y-axis are labeled, with the x-axis ranging from 0 to 8 and the y-axis from 0 to 8.

This setup is used to find the volume of a solid of revolution by rotating the triangular region around an axis, utilizing the shell method.
Transcribed Image Text:**Transcription for Educational Website:** Title: Using the Shell Method to Evaluate Volumes Instructions: Use the shell method to write and evaluate the definite integral. Equation: \( y = 8 - x \) Response: \(-1\) ❌ --- **Diagram Explanation:** The graph displays a triangular region under the line \( y = 8 - x \) on the coordinate plane. The triangle is shaded in blue and bounded by the x-axis from \( x = 0 \) to \( x = 8 \), and the y-axis. - The hypotenuse of the triangle is the graph of the equation \( y = 8 - x \), which intersects the x-axis at \( (8, 0) \) and the y-axis at \( (0, 8) \). - There is a vertical yellow rectangle within the triangle at \( x = 4 \), representing a typical shell or element used in setting up the integral for the shell method. - The x-axis and y-axis are labeled, with the x-axis ranging from 0 to 8 and the y-axis from 0 to 8. This setup is used to find the volume of a solid of revolution by rotating the triangular region around an axis, utilizing the shell method.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,