Question

let y=∫_1^cos(x) (3t+2sin(t))dt. Use the Fundamental Theorem of Calculus to find y′.
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Answer 1

\[\Large

f(x)=\int_1^{u(x)} g(t) dt \\
\Large
f'(x)= g(u(x) u'(x)
\]

Answer 2

in your case
\[
u(x) = \cos(x)\\
g(t)= 3 t + 2 \sin(t)

\]

Answer 3

The answer is
\[
-3 \sin (x) \cos (x)-2 \sin (x) \sin (\cos (x))

\]

Answer 4

thank you so much!!!!