8.7.1. Use partial fractions to evaluate the integral dr r(1-r2) that arises in Example 8.7.1, and show that ri = [1+ e-4" (rj² – 1)]¬1/2. Then confirm that P'(r*) = e-4T, as expected from Example 8.7.3.
8.7.1. Use partial fractions to evaluate the integral dr r(1-r2) that arises in Example 8.7.1, and show that ri = [1+ e-4" (rj² – 1)]¬1/2. Then confirm that P'(r*) = e-4T, as expected from Example 8.7.3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The value of the
I just need help in showing that the value of r1 is what is given.
![**8.7.1.** Use partial fractions to evaluate the integral \(\int_{r_0}^{r_1} \frac{dr}{r(1-r^2)}\) that arises in Example 8.7.1, and show that \(r_1 = \left[1 + e^{-4\pi}(r_0^{-2} - 1)\right]^{-1/2}\). Then confirm that \(P'(r^*) = e^{-4\pi}\), as expected from Example 8.7.3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88e1e2e4-888b-4182-8c02-fd46dda7f6b1%2F61b1b100-5ab1-47e8-9d1f-cc4ac2b6f9d4%2Fw96a0bk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**8.7.1.** Use partial fractions to evaluate the integral \(\int_{r_0}^{r_1} \frac{dr}{r(1-r^2)}\) that arises in Example 8.7.1, and show that \(r_1 = \left[1 + e^{-4\pi}(r_0^{-2} - 1)\right]^{-1/2}\). Then confirm that \(P'(r^*) = e^{-4\pi}\), as expected from Example 8.7.3.
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