Question

If y = 5 + integral (2, 2x) of e^2 dt
then dy/dx = ?

Answer 1

\[y=5+\int\limits_{2}^{2x}e ^{-2}dt\]

Answer 2

This could be rewritten as:
\[y=5+e ^{-2}\int\limits\limits_{2}^{2x}dt\]

Answer 3

Oh, right! Because e is a coefficient.

Answer 4

\[y = 5 + e^{-2}[t]_{2}^{2x}\]

Answer 5

you know the rest right

Answer 6

Oh, so you simply take the antiderivative of dt?

Answer 7

let me finish the answer so it gets clearer for you
\[y = 5 + e^{-2}[2x-2]=5+2e^{-2}[x-1]\]

Answer 8

Hmm I didn't realize you could manipulate the dt in the integral - thank you very much!

Answer 9

you are more than welcome!