Question

How do I evaluate the following integral:

int[(sqrt(11/x))]dx limits of integration are 36 to 1 (top to bottom)

Answer 1

\[\huge \int\limits_{1}^{36}\sqrt{\frac{11}{x}}dx\]
This?

Answer 2

Let's leave the evaluating the limits part for later. For now, focus on
\[\int\limits_{}^{}\sqrt{\frac{11}{x}}dx\]
Which is just the same as
\[\int\limits_{}^{}\frac{\sqrt{11}}{\sqrt{x}}dx=\sqrt{11}\int\limits_{}^{}\frac{1}{\sqrt{x}}dx=\sqrt{11}\int\limits_{}^{}x^{-\frac{1}{2}}dx\]
And perhaps this is easier to evaluate.

Answer 3

Wowwwwww. How do you recognize that? I don't even fully know what you're doing right there. That's just simple algebra right? It does make the problem much easier to evaluate.

Answer 4

Okay so now I can set u = x, du = \[2x ^{\frac{ 1 }{ 2 }}\]

and then from there use the ftc?

Answer 5

looks like webassign to me

Answer 6

you do not need a u - sub, find the anti derivative directly

Answer 7

the anti derivative of \(\frac{1}{\sqrt{x}}\) is \(2\sqrt{x}\) you can check by differentiation

Answer 8

yeah duh you're right. wow. there's literally not even chain rule in there because he showed me that you can simplify it... okay i'll start using my head now