## anonymous 4 years ago HELP ME WITH DEFINITE INTEGRALS, AND THE FUNDAMENTAL THEOREMS OF CALCULUS PLEASE!!

1. anonymous

IF g(x) = $\int\limits_{1}^{2lnx} e^t/\sqrt{1+e^(2t)} dt,$ find g'(x)

2. anonymous

should be e^(2t)

3. anonymous

take the derivative using the chain rule. basically replace t by $2\ln(x)$ in the integrand, and then multiply by $\frac{2}{x}$ the derivative of $2\ln(x)$

4. anonymous

what would be the final answer to this question? just to see if i got it correct. i got 4...?

5. anonymous

wrong question. i got 2x/(1+x^2)

6. anonymous

$\frac{e^{2\ln(x)}}{\sqrt{1+e^{4\ln(x)}}}\times \frac{2}{x}$cleans up a great deal

7. anonymous

$\frac{x^2}{\sqrt{1+x^4}}\times \frac{2}{x}$

8. anonymous

i got that but you would multiply the 2 terms together?

9. anonymous

would you*

10. anonymous

if $f(x)=\int\limits_{4/x}^{16} (3\div(4+t^3))dt$, find f'(x)