Integral Shortcuts

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^(x²)

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

Originally Posted by I Took the Red Pill ^

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.

Xaven Missing. Location: Alt + F4	#1 Integral Shortcuts 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
02-06-2008, 06:03 AM

Flying Mullet Site Staff Cid's Knight this space for rent Location: Finding my monkey cage exit strategy	#2 (permalink) Sorry, I'm not following. Are you asking what the integral of the following formula is? F(t) = c^(x²)
02-06-2008, 12:30 PM

Aerith's Knight The last real knight Location: The Netherlands	#3 (permalink) 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
02-06-2008, 02:12 PM

I Took the Red Pill bowowowyippieyoyippieyay Location: Central New York	#4 (permalink) 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.
02-06-2008, 10:29 PM

Tavrobel By the dog, Gorgias. Location: Conjunction Junction	#5 (permalink) That looked more like the Chain Rule than integration.
02-07-2008, 01:54 AM

Xaven Missing. Location: Alt + F4	#6 (permalink) Originally Posted by I Took the Red Pill ^ 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.
02-08-2008, 07:08 AM