Question

integrate sin^2x / sqrt x dx

Answer 1

We'll replace (sin x)^2 = (1-cos 2x)/2
Int (1-cos 2x)dx/2sqrt x = Int dx/2sqrt x - Int cos 2x dx/2sqrt x
Int (1-cos 2x)dx/2sqrt x = sqrt x - Int cos 2x dx/2sqrt x
We'll integrate by parts Int cos 2x dx/2sqrt x using formula
Int udv = u*v - Int vdu

Answer 2

that still won't work

http://www.numberempire.com/integralcalculator.php?function=cos%282x%29%2F%282*sqrt%28x%29%29&var=x&answers=&__utma=164170016.165112442.1306893325.1311847678.1311849610.5&__utmz=164170016.1311849611.5.4.utmcsr%3Dgoogle |utmccn%3D%28organic%29|utmcmd%3Dorganic|utmctr%3Dintegral+calculator&screen_height=768&__utmc=164170016&__utmb=164170016.3.10.1311849611

Answer 3

This seems to be one of those u keep getting an integral that is as difficult as the one u started with.

Let me look around, see if there is some tricky way around it.

Answer 4

ok :(

Answer 5

i am having a test and this is a hint

Answer 6

Normally u would do integration by parts twice and then use the result of the second integration to subback which I am just having a look at now but seems I have to go at least 3 times....:-(

Answer 7

:(

Answer 8

I can't be doing all the calculations (doing my head in) but if u use georgia's substitution and integrate by parts twice u will go from Cos 2x to Sin 2x and back to Cos 2x so u should be able to substitute from the first to the last for an answer (I think)

Else u will have to wait for the calc wiz's to arrive, sorry...

Answer 9

im telling you there is no solution using elementary functions, the anti-derivative involves the error-function

Answer 10

Strange they would give such a thing in a test, though...

Answer 11

i hope not... he said::: could be in the test

Answer 12

Multiple choice? D-no solution...:-)

Answer 13

jajajaja

Answer 14

hmm i dunno...you have a point though
is there more to this problem?

Answer 15

what u mean?

Answer 16

I am going to have to try what I said, I hate number crunching.

Where's satellite, he loves this sort of stuff...

Answer 17

is it a definite integral?

Answer 18

i read to solve this problem they use rengels,, something like that

Answer 19

yes

Answer 20

from 0 to pi

Answer 21

oh ok, then you can evaluate it using numerical methods. Even graph it in a graphing calculator then estimate area from 0 to pi

Answer 22

Like 1 and a bit...

Answer 23

yeah...i get 1.34

Answer 24

dumbcow looks right, the problem is the powers of x go up so there is no exact substitution that I can see.

I don't know why they bother with all this stuff anyway, real world integrals never work like the ones in the books...:-) They are nearly always have to be solved numerically.
Must be for pure math people.

Answer 25

:(