Question

help please i need someone to explain

Find S d/dx cosx^2 dx=

Answer 1

\[\int\limits_{}^{}\frac{ d }{ dx }cosx^2dx\]

Answer 2

\(\Large I (x) = \int\limits_{}^{}\frac{ d }{ dx }cosx^2 \; dx\)
\(\Large = \frac{ d }{ dx } \int\limits_{}^{}cosx^2 \; dx\)

the integral and the derivative are "inverses". in the sense that one leads to the other, and vice versa.

and this simple idea has a very fancy name:

https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

Answer 3

so to restate:

\[\Large \int\limits_{}^{}\frac{ d }{ dx }cosx^2 \; dx = \frac{ d }{ dx } \int\limits_{}^{}cosx^2 \; dx\]

or, in plain-speak, the integral of the derivative equals the derivative of the integral.

Answer 4

so would the answer be cosx^2 since the d/dx and Sdx cancels?

Answer 5

well, sort of or mostly or maybe not...i was being very hand-wavey to get the point across.

the bad boy in the room is the integration constant

http://www.wolframalpha.com/input/?i=d%2Fdx+%5Bcos%28x%5E2%29%5D

http://www.wolframalpha.com/input/?i=integrate+-2x+sin%28x%5E2%29

these are indefinite integrals.

it can all be worked around but your question is quite specific so i think that means you need to countenance the integration constant and factor that into your thought process.