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 fe-x² dx fe-y²dy into polar coordinates and you'll end up with a function that can be integrated easily.) .

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 49E
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[Second Order Equations] How do you solve question six thank you

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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