Question

Can someone help me determine F'(x) when
F(x) = (intergal) from x to 0 (4 cos^5(2πu)) du

a. F′(x) = −5 sin(2π)x cos^4(2πx)
b. F′(x) = 8π cos^5(2πx)
c. F'(x) = −5π sin(2πx) cos^4(2πx)
d. F′(x) = −4 sin^5(2πx)
e. F′(x) = 8π cos^4(2πx)
f. F′(x) = 4 cos^5(2πx)

Answer 1

We are looking to take the derivative of this function:
\( \displaystyle F(x) = \int_{x}^{0} 4 \cos ^ 5 (2 \pi u ) \ du \)
So...
\( \displaystyle F' (x) = \dfrac{d}{dx} \int_{x}^ {0} 4 \cos^5 (2 \pi u) \ du \)
Does this look like any identities or theorems you have seen before?

Answer 2

yea! i got it now i think i know the answer thank you (: @AccessDenied

Answer 3

No problem! :)

Answer 4

Is it written as \( \int_{0}^{x} \) in the problem? If it is \( \int_{x}^{0} \), the answer doesn't seem to be present unless there is a typo. IWe'd have to switch the order of integration to apply fundamental thm: \(\int_{x}^{0} = -\int_{0}^{x} \) if it is indeed that way.

Answer 5

it was from 0 to x lol! @AccessDenied

Answer 6

Ah, got it!
Then that makes sense. :p