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#1 2007-05-21 03:57:12

fangree01
Member
Registered: 2006-11-13
Posts: 11

Integration

Hi,

I was wondering if someone could tell me if I have done this question right?

∫ xe^-4x² dx

OK I made u=4x² to get du=8x and rewrite as xdx=1/8du.  I am not sure if i should have made these negative or not so I went with not.

The answer I got is -1/32 e^-4x² + c.

I am just not sure about the negative thing and if I have intergated the e part right.  dizzy

I would be grateful for any help.

Thanks

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#2 2007-05-21 04:34:16

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Integration

The correct answer is

Checking integration answers is very easy – just differentiate your answer and see if you get the original expression back.

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#3 2007-05-21 07:36:06

fangree01
Member
Registered: 2006-11-13
Posts: 11

Re: Integration

Hi JaneFairfax,

Thanks for your help and tip I keep forgetting about differentiating to see if I have the right anwser. 

Can I just double check something though  when you integrate someting like e^4x the answer comes out as 1/4 e^4x + C so I was wondering why this did not happen in this question?  This is where I got the -1/32 e^-4x² + c answer, or does this only happen if the question is not a change of variable?

Thanks again for your help up

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#4 2007-05-21 07:46:41

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Integration

After changing your variables, your integral became ∫1/8e^-udu.
There wasn't any coefficient in the power of e any more, so you only needed to divide by -1, not -4.


Why did the vector cross the road?
It wanted to be normal.

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#5 2007-05-21 07:49:55

fangree01
Member
Registered: 2006-11-13
Posts: 11

Re: Integration

Hi Mathsyperson,

Thanks for your help, I knew it would be something I was overlooking or looking to hard at dizzy

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