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Question

bmk614 · Answer

Let f be the function given by $$f(t)=\int\limits_{0}^{t} e^{xcos(x)}[\cos(x)-xsin(x)]dx, 0 \le t \le 10.$$At which of the following values does f attain its absolute maximum value?
A) 0.860
B) 3.426
C) 6.437
D) 9.529
E) There is no absolute maximum value

bmk614 · Answer

@zepdrix @dumbcow @inkyvoyd @UsukiDoll

bmk614 · Answer

@Zarkon @across @matlee

dumbcow · Answer

For this problem, i recommend doing the integral and getting function f(t)
Then graph function to look for local maximums, whichever is greatest is your absolute max

dumbcow · Answer

use u -substitution .... notice that cos - xsinx  is derivative of xcosx

bmk614 · Answer

Do you know what the integral would be?

dumbcow · Answer

u = x cos(x)
du = cos(x) - x sin(x) dx

$$f(t) = \int\limits_0^t e^u du = |_0^t e^{x \cos x} = e^{t \cos t} - 1$$

bmk614 · Answer

Thank you so much!!! I didn't even think of u du substitution.

dumbcow · Answer

yw