Find the derivative of the following function
F(x)=the integral from x^5 to x^3 of (2t-1)^3 dt
I will write it in a formula form below in the next box

Question

Find the derivative of the following function 
F(x)=the integral from x^5 to x^3 of (2t-1)^3 dt
I will write it in a formula form below in the next box

anonymous · Answer

$$F(x)=\int\limits_{x^5}^{x^3}(2t-1)^3 dt$$

anonymous · Answer

This implements the fundamental theorem of calculus.$$\frac{ d }{ dx } \int\limits_{0}^{f(x)}g(t) dt=g(f(x)*f ^{'}(x)$$

anonymous · Answer

$$F(x)=\int\limits_{x5}^{x^3}(2t−1)^3dt=\int\limits_{0}^{x^3}(2t−1)^3dt - \int\limits_{0}^{x^5}(2t−1)^3dt $$
$$f(x)=3(2x^3-1)^3x^2-5(2x^5-1)^3x^4$$

anonymous · Answer

The trick the the FTC is that the lower limit must be equal to zero. If it isn't the integral must be separated into two separate integrals as above.

anonymous · Answer

Thank you sooooooo much for your help!

anonymous · Answer

Is there anything you are confused about or would like more help with?
and of course, you are quite welcome

anonymous · Answer

I think I am good but I guess I will find out as I progress through my homework LOL