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6. Compute fe-x² dx. (Hint: This is a function that cannot be integrated by formula. So use the following trick. Transform the double integral fo°º° e¯x² dx · f°° e-y²dy into polar coordinates and you'll end up with a function that can be integrated easily.)

6. Compute fe-x² dx. (Hint: This is a function that cannot be integrated by formula. So use the following trick. Transform the double integral fo°º° e¯x² dx · f°° e-y²dy into polar coordinates and you'll end up with a function that can be integrated easily.)

Advanced Engineering Mathematics
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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[Second Order Equations] How do you solve question 6?

6. Compute fe-x² dx. (Hint: This is a function that cannot be integrated by formula. So use the following trick. Transform the double integral foe-x² dx · fe-y²dy into polar coordinates and you'll end up with a function that can be integrated easily.) 7. Use Exercise 6 to show that fe-¹² dp = √√√. Then substitute p = x/√4kt to show that Lo S(x, t) dx = 1.
Transcribed Image Text:6. Compute fe-x² dx. (Hint: This is a function that cannot be integrated by formula. So use the following trick. Transform the double integral foe-x² dx · fe-y²dy into polar coordinates and you'll end up with a function that can be integrated easily.) 7. Use Exercise 6 to show that fe-¹² dp = √√√. Then substitute p = x/√4kt to show that Lo S(x, t) dx = 1.
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