Integral Shortcuts

[Xaven]

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]

Sorry, I'm not following. Are you asking what the integral of the following formula is?

F(t) = c^(x²)

[Aerith's Knight]

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]

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]

That looked more like the Chain Rule than integration.

[Xaven]

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.