Question

Derivative of integrals?

Answer 1

\[\frac{d}{dx}\int_{a}^{x}f(t)\space dt=f(x)\\f(x) = \frac{e^x}{x}\]
you have
\[\frac{d}{dt}\int_{t}^{2}\frac{e^x}{x}\space dx=-\frac{d}{dt}\int_{2}^{t}\frac{e^x}{x}\space dx=-f(t) = -\frac{e^x}{x}\]

Answer 2

One correction @zzr0ck3r...the x should be a t...I know picky but it should

Answer 3

right

Answer 4

I copied it from above:)

Answer 5

\[-\frac{e^t}{t}\]

Answer 6

@lizmariej do you see how this worked?

Answer 7

All we really had to do was flip the bounds. Then the Fundamental Theorem of Calculus did all the work.

Answer 8

Yes, thankyou.

Answer 9

so if the bounds were from a to x, we would have just wrote f(t) as the answer...no work needed.

Answer 10

or in your case 2 and t