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Integral Help Please! Fundamental Theorem of Calculus Questions!?
1. If f(x)= the integral of t^3 dt from x to 12 then the derivative of f(x)=?
2. Find the derivative of the following function?
F(x)= (2t-1)^3 dt from x^3 to x^4
1 Answer
- Anonymous9 years agoFavourite answer
1.
FTC: d/dx of an integral from any constant to x : plug the x into the function inside the integral
Find: d/dx of the integral from x to 12 of t^3
First, we flip the integral and let it go from 12 to x instead. In doing so, we must flip the sign of the answer we get.
By FTC, plugging in x into the function t^3 gives us x^3. And now flip the sign to get - X^3.
f'(x) = -x^3
2.
FTC: when the limits of your integral = u, plug u into the function for t and multiply by u' (chain rule).
d/dx from x^3 to x^4 of (2t-1)^3 dt
=[4x^3(2x^4 - 1)^3] - [3x^2(2x^3 - 1)^3]