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Xaven
02-06-2008, 06:03 AM
Calculus!:
When dealing with definite integrals and using the second fundamental theorem of calculus would...
Integral from c to x^2 of F(t)
just be
F(x)*2x?
Replace the Ts or other variables with Xs and multiply by the derivative of the top number of the integral sign? Sorry for lack of pretty font. :P
Flying Mullet
02-06-2008, 12:30 PM
Sorry, I'm not following. Are you asking what the integral of the following formula is?
F(t) = c^(x<sup>2</sup>)
Aerith's Knight
02-06-2008, 02:12 PM
and from what i can tell thats pretty much differentiating.. not intergrating..
if you have a x^2 term in an intergral.. there should always be a 1/3 x^3 term in the answer
I Took the Red Pill
02-06-2008, 10:29 PM
F(x)= ∫ F(t) dt on the interval [c,x²], correct?
F'(x) = 2xF(x)
F(x) ≠ 2xF(x)
The Second Fundamental Theorem of Calculus allows you to do what you did to find the derivative of the anti-derivative of the function with respect to x, not the integral. So the way you phrased it, no.
Tavrobel
02-07-2008, 01:54 AM
That looked more like the Chain Rule than integration.
Xaven
02-08-2008, 07:08 AM
F(x)= ∫ F(t) dt on the interval [c,x²], correct?
F'(x) = 2xF(x)
F(x) ≠ 2xF(x)
The Second Fundamental Theorem of Calculus allows you to do what you did to find the derivative of the anti-derivative of the function with respect to x, not the integral. So the way you phrased it, no.
Oh yes, yes. I see.
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