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How do I integrate (4a^2 x^6)*e^(-x^2) from zero from infinity.

0 votes

where a (alpha) is constant?

asked Nov 5, 2014 in CALCULUS by anonymous

1 Answer

0 votes

Given function : 4a2x6ex2

image

First derive general solution for image

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Let u = x2n-1

u =(2n-2) x2n-2

Let dv=xex2

v = -½ ex2

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Continue in comment ...........

answered Nov 5, 2014 by lilly Expert

Continue from solution..............

Changing to polar coordinates : image

image

image

If r2 = u then rdr = du/2
image

Here angle gives π degrees.So

image

image

image

image

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From hypothesis rule f is at 0 and n are derived

The general solution image

Given problem is

Here n=3

image

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The solution is 4a2x6ex2 dx = (15/16)√π

 

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