Question

HELP ME WITH DEFINITE INTEGRALS, AND THE FUNDAMENTAL THEOREMS OF CALCULUS PLEASE!!

Answer 1

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

Answer 2

should be e^(2t)

Answer 3

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
\[2\ln(x)\]

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

would you*

Answer 10

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