## anonymous 5 years ago How do you find the differential of the integral cos^3(x) dx from -9ts to -5t+6s?

1. anonymous

$\int\limits_{-9ts}^{-5t+6s}\cos ^{3}(x) dx$

2. amistre64

ummmm......... i dont really know...

3. amistre64

i spose its possible, just use those"equations" as the F(x) stuff in the end

4. amistre64

you might want to go about "reducing" the integrand to an addition of sin and cos....maybe

5. amistre64

cos cos^2 cos(1-sin^2) cos(x)(1 - (1-cos(2x)/2)) ... along those lines eh?

6. anonymous

yeah thats what i was going to say

7. amistre64

well say it again then :)

8. anonymous

integral of sin^2 is known as -x/2 + sincos/2 so you could use that

9. anonymous

Well I have notes and an example problem, but it doesnt really make sense. He has the differential of the integral e^-x^2 from a to b. He then takes partials. Fa = -e^a^2 and Fb = e^b^2. Then apparently the differential is -e^a^2 * da + e^b^2 * db. No sense.

10. anonymous

Don't worry about it, I just wondered if anyone could make sense out of it, but obviously my teacher is drunk. He wrote his own "textbook" in Mathematica and he didn't do a very good job.

11. anonymous

are you still talking about integral of cos^3? anyway yeah there are no elementary functions to describe integral of e^(-x^2).