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... from Calculus I.
![[image loading]](http://img441.imageshack.us/img441/5273/fundthm.png)
I was taking a practice test for the GRE-Math subject test and it threw me this curveball. I didn't know what to do. I was like hiding behind my chair in the library and shit. People were staring man. This shit scared me.
Even though I knew it didn't make any sense, I told myself that it was D because if I just pretend that x+t becomes x+x then it works out all nice and pretty-like to become D.
So the answer is apparently E according to Mathematica and the practice test answer key, but I have no clue how they got to it.
So clearly I'm forgetting something about the Fundamental Theorem... even though I went through the wikipedia page a little bit before posting here. I was going to do it on reddit but they won't let me make a new link for another hour because of some bullshit email verification crap.
![[image loading]](http://img827.imageshack.us/img827/2876/78156151.png)
 
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United States4053 Posts
+ Show Spoiler +
Ok my usual method gives me BS since the integrand has an x in it, so try this
Bring the E^x out of the integral to get E^x * integral from 0 to x^2 of (E^t dt), which is E^x * (E^(x^2) - 1) = E^(x + x^2) - E^x. Derivative is (1+2x) * E^(x + x^2) - E^x. Plug in 1 to get 3*E^2 - E
... i think. Calculus was so long ago
EDIT: wtf the t did not disappear, let me fix this
EDIT 2: fixed
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Netherlands4989 Posts
I thought you were a forge, I am disappoint 
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since e^x is independent with regards to t, move it outside. Then integrate e^t. Obviously it is e^t. Evaluating in those points, we get e^x¨2-1. All that must be multiplied with the e¨x we moved outside at the beginning. we get e¨(x¨2+x)-e¨x. Derive for x, don't forget inner derivate, and it should become (2x+1)e¨(x¨2+x)-e¨x. Evaluate for x=1. Sorry for potentially incorrect English.
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On September 20 2010 07:42 Saechiis wrote:I thought you were a forge, I am disappoint
"clearly I'm forge" fast expanding??!
ok disappoint but I'll take calculus too. as stated e^(x+t) = e^x*e^t and you can take e^x outside the integral and apply the fundamental theorum of calculus to get the derivative at 1
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Wtf is everyone talking about.
Fundamental theorem of calculus part 1, look it up.
The derivative of an integral is the integrand itself.
Your answer is B
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On September 20 2010 09:58 Rev0lution wrote:
Wtf is everyone talking about.
Fundamental theorem of calculus part 1, look it up.
The derivative of an integral is the integrand itself.
Your answer is B
you're taking the derivative with respect to x, not t
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Lol tricky bastards, didn't see that it was h-prime and not just plain old h xD. those test creator guys are evil  thought it was B the whole time lol.
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OK,
Here is what you need to do. Use Leibniz Rule. Take first the derivative of the function h wrt to x by applying Leibniz Theorem and then evaluate it at x=1. Mathematica is correct and the correct answer is (E).
Here is the link to wikipedia page on Leibniz Rule:
http://en.wikipedia.org/wiki/Leibniz_integral_rule
That's a single most important tool when dealing with some nasty integrals that contain parameters.
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On September 20 2010 07:54 Fwmeh wrote:
since e^x is independent with regards to t, move it outside. Then integrate e^t. Obviously it is e^t. Evaluating in those points, we get e^x¨2-1. All that must be multiplied with the e¨x we moved outside at the beginning. we get e¨(x¨2+x)-e¨x. Derive for x, don't forget inner derivate, and it should become (2x+1)e¨(x¨2+x)-e¨x. Evaluate for x=1. Sorry for potentially incorrect English.
When in doubt, use images:
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On September 20 2010 07:54 Fwmeh wrote:
since e^x is independent with regards to t, move it outside.
HAHA!
I knew it was something so simple! That's all I needed to see.
Oh man I feel really stupid right now. Lovely trick, playing on my preconceptions.
I love mathematics
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sorry, cant help ya. just like 96% of the public, i suffer from severe mathophobia
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EPT
