Question

Please help me evaluate the following interval (click to see) using an appropriate substitution.

Answer 1

\[\int\limits_{}^{}\frac{ dx }{ \sqrt{x}e ^{(16\sqrt{x})} }\]

Answer 2

just realized i wrote interval and not integral

Answer 3

\[u = 16\sqrt{x}\]\[du =\frac{ 8 dx }{ \sqrt{x} }\]\[8\int\limits_{}^{}\frac{ du }{ e ^{u} }\]

Answer 4

So, just solve the new integral and resubstitute for the expression for x.

Answer 5

ok, and what does dx equal? Just so I know how to solve for dx...

Answer 6

That's in the second of the three equations I determined.

Answer 7

Right, I do not know how to solve for dx

Answer 8

You are in calculus, therefore, I'm sure you know basic arithmetic. Just rearrange the second equation. The three equations I wrote flow logically one to the next.

Answer 9

oh ok i see now... nvm

Answer 10

hold on.

Answer 11

My last equation is a little off, it should be\[\frac{ 1 }{ 8 }\int\limits_{}^{}\frac{ du }{ e ^{u} }\]

Answer 12

ok thanks

Answer 13

uw!