d/dx integral from o to x of function cos(2*pi*x) du is
first i do the integral and i find the derivative right.
by the fundamental theorem of calculus, if there is an integral from o to x, don't i just plug the x in the function.
the integral of the problem is cos*2*pi*) is just cos(2*pi*x) right or is that wrong. then i find the derivative.
I'm not sure. I think it's sin(2pi), but you can check out calc101 (google it) for help..?
Been a while
To find the derivative of the integral, you can start by applying the Fundamental Theorem of Calculus. According to this theorem, if we have an integral of the form ∫[a to x] f(u) du, where f(u) is a continuous function and x is a variable, then the derivative of this integral with respect to x is simply the integrand evaluated at x.
In this case, we have ∫[0 to x] cos(2πu) du. Applying the Fundamental Theorem of Calculus, the derivative with respect to x is equal to cos(2πx).
So, your initial intuition is correct. The derivative of the integral with respect to x is cos(2πx).
If you still have doubts or would like to check your answer using an online tool, Calc101 can be a helpful resource. You can search for "Calc101" on Google and it will take you to their website. There, you can input the function and find its derivative or integral.