Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If r than one method applies, use whatever method you prefer. In 5 0 6x 。 -2 -6/x e dx Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. The integral converges because OB. The integral diverges because In 5 0 In 5 0 - 6/x 6x 2e -2-6/x 6x .... dx = dx =
Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If r than one method applies, use whatever method you prefer. In 5 0 6x 。 -2 -6/x e dx Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. The integral converges because OB. The integral diverges because In 5 0 In 5 0 - 6/x 6x 2e -2-6/x 6x .... dx = dx =
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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![**Transcription for Educational Website**
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**Convergence Test for Integral**
Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer.
\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx \]
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**Multiple Choice Question**
Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.)
- **A.** The integral converges because
\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \]
- **B.** The integral diverges because
\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \]
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**Instructions for Students:** Analyze the integral using your preferred method of convergence testing. Provide the final answer in the space provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47f16b03-5eea-43fc-9b52-7dcc57452af9%2F00bbe62a-7f04-460f-8ee0-936ad638c16b%2Fnxsd0id_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
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**Convergence Test for Integral**
Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer.
\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx \]
---
**Multiple Choice Question**
Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.)
- **A.** The integral converges because
\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \]
- **B.** The integral diverges because
\[ \int_{0}^{\ln 5} 6x^{-2} e^{-6/x} \, dx = \, \_\_ \]
---
**Instructions for Students:** Analyze the integral using your preferred method of convergence testing. Provide the final answer in the space provided.
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