Question

Find the integral of (lny)/(squareroot y) and evaluate at 81 and 64

Answer 1

seems like an integration by part problem to me.

Answer 2

I tried that and got \[((2x ^{1/2}*\ln(x))-4x ^{1/2}\] but I'm not sure if that's right

Answer 3

got an idea how to start such a problem?

\[ \large \int \ln x \frac{1}{\sqrt{x}}dx= \int \ln x \cdot x^{-\frac{1}{2}}dx \] from here on use integration by parts.

Answer 4

\[ \Large 2 \sqrt{x} \ln x - 4 \sqrt{x} = 2\sqrt{x}(\ln x -2 )\]

Answer 5

so you are right yes.

Answer 6

when I try inserting the values in I'm having a little trouble

Answer 7

would you take the equation and insert 81 into it and minus that whole thing by the same equation but with 64 inserted?

Answer 8

That's why I tried to simplify the expression, I haven't inserted the values yes though. It wont be a pretty number in the end anyway from what I can tell, because of the natural log.

Answer 9

yes that's how it works @danielleg

Answer 10

First insert the higher values of x and calculate, then minus the lower bound of the integral evaluated at said bound.

Answer 11

I did that and eventually got 124.859

Answer 12

but that isn't right

Answer 13

\[ \large \approx 8.55 \]

Answer 14

when I submitted that into the test it said it was wrong and gave it all in ln but when I put their answer into my calculator it came out to the same thing you got so maybe I'll send my teacher a message

Answer 15

oh well I understand that, maybe they want the EXACT result, the exact result is of course in form of natural log.

Answer 16

\[ \Large 18(\ln81-2)-16(\ln64-2) \approx 8.5579 \]

Answer 17

you can simplify that expression even more, most of the time when you are dealing with integrals they don't request the exact result.

Answer 18

oh ok thank you very much for your help

Answer 19

welcome