Question

Can someone help with this integral?

Answer 1

\[\frac{d}{dx}\int\limits_{1}^{2x}f(t) dt=\frac{d}{dx}[\int\limits_{1}^{2x}f(t) dt]\]
\[=\frac{d}{dx}[F(t)]_1^{2x} \text{ where } F'=f\]
\[=\frac{d}{dx}[F(2x)-F(1)]=\frac{d}{dx}F(2x)-\frac{d}{dx}F(1)\]
Use the chain rule and constant rule to find the derivative of F(2x) and F(1)

Answer 2

I don't really understand

Answer 3

That integal sign means you integrate which i did

Answer 4

then i plug in my upper limit and my lower limit and found the difference

Answer 5

which was F(2x)-F(1)

Answer 6

we were asked to find the derivative of the integral

Answer 7

so that is the last step we are on

Answer 8

Can you show the steps? I cannot get the correct answer

Answer 9

I integrated f and called it F
then I plugged in my upper limit minus plug in my lower limit
of my work above that i showed can you tell me what part troubles you

Answer 10

I got it thank you !!!