Question

i need help with this problem. I will post a picture of it :)

Answer 1

hi!!

Answer 2

chain rule for this one

Answer 3

hey. could u show me ?

Answer 4

that didn't come out quite right
replace the \(t\) in \(1+\cos(t)\) by the upper limit if integration \(x^2+2\)
then multiply by the derivative of \(x^2+2\)

Answer 5

you got that?

Answer 6

uhm do i take the derivative of cos?

Answer 7

nope

Answer 8

the fundamental theorem of calculus sez the derivative of the integral is the integrand
if it was
\[\int_0^x(1+\cos(t))dt\] then the derivative would be
\[1+\cos(x)\]

Answer 9

but you have
\[\int_0^{x^2+2}(1+\cos(t))dt\] which is a composite function
replace \(t\) by \(x^2+2\) is all, then multiply by \(2x\) because that is the derivative of \(x^2+2\)

Answer 10

so the answer is 2xsqrt cos(x^2+1) ?

Answer 11

my bad i mean 2x sqrt cos(x^2+2)+ 1

Answer 12

hold on let me check

Answer 13

yeah \[2x\sqrt{\cos(x^2+2)+1}\]

Answer 14

okay

Answer 15

thanks :)

Answer 16

what @misty1212 said

Answer 17

alright thanks