chloeaj95
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#1
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#1
Steps please
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chloeaj95
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#2
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(Original post by alow)
Do you mean this?

\[\int {2y \times {e^{2y}}dy} \]

If so, use integration by parts.
No the e is y^2 not 2y

I've tried integration by parts but I just go round in circles
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alow
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(Original post by chloeaj95)
No the e is y^2 not 2y

I've tried integration by parts but I just go round in circles
EDIT: Look at what ghostwalker said, I was being a bit blonde.
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Old_Simon
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#4
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Are you sure e^y^2 can be integrated at all?
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ghostwalker
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#5
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(Original post by chloeaj95)
Steps please
Since you can't see it by recognition, use substitution.


Let u=y^2

I presume it's \displaystyle\int 2ye^{y^2}\;dy
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the bear
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no if you substitute u = 2y then the integration by parts works fine...
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ztibor
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#7
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(Original post by chloeaj95)
Steps please
The derivative of e^{y^2} using the chain rule is

\displaystyle \frac{d}{dy} \left (e^{y^2} \right )=e^{y^2} \cdot 2y

Then the undetermined integral of e^{y^2}\cdot 2y is ...?


Generally when

 \displaystyle  \int f(x) dx = F(x) +C

then for composite f[g(x)]

\displaystyle \int g'(x) \cdot f[g(x)] dx=F[g(x)] +C

Your composition is from  f(y)=e^y and g(y)=y^2

AS g'(y)=2y
THe type of this integral is
\displaystyle \int g'(y) \cdot f[g(y)] dy
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interstitial
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#8
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If we let u= y^2, then using IBS, you get \displaystyle\int e^u \mathrm d u.
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davros
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#9
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(Original post by chloeaj95)
Steps please
Use substitution u = y^2. After a while you should be able to do this integral by recognition because it involves the exact derivative of a function.
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davros
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#10
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(Original post by majmuh24)
If we let u= y^2, then using IBS, you get \displaystyle\int e^u \mathrm d u.
I hope you mean IBP, otherwise the OP is in real trouble
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james22
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#11
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Why are some people saying intergration by parts? This is a simple substitution question.
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interstitial
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#12
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(Original post by davros)
I hope you mean IBP, otherwise the OP is in real trouble
:ninja: I was lazy and couldn't be bothered to write the whole phrase, but that won't happen again :hat2:

Posted from TSR Mobile
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davros
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(Original post by james22)
Why are some people saying intergration by parts? This is a simple substitution question.
I think some people were confused by the lack of latex. It's either a straightforward substitution or recognition.
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TenOfThem
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#14
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(Original post by davros)
I hope you mean IBP, otherwise the OP is in real trouble
IBS was correct that poster used substitution not parts
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interstitial
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#15
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For anyone who needs it cleared up, I believe the OP meant 2y e^{y^2}

Posted from TSR Mobile
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TenOfThem
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(Original post by james22)
Why are some people saying intergration by parts? This is a simple substitution question.
Not even substitution is needed, recognition (inverse chain rule)
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L'Evil Fish
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#17
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I swear the answer is just

e^(y^2)

:emo:
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davros
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#18
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(Original post by TenOfThem)
IBS was correct that poster used substitution not parts
IBS = Irritable Bowel Syndrome

I've never seen it used as an abbreviation in mathematics
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TenOfThem
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#19
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(Original post by L'Evil Fish)
I swear the answer is just

e^(y^2)

:emo:
It is
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TenOfThem
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#20
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(Original post by davros)
IBS = Irritable Bowel Syndrome
I agree

I've never seen it used as an abbreviation in mathematics
Me neither but it was more correct than IB in this case
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