Question

integral of sin(x^1/2)

Answer 1

\[\int\limits_{}^{}\sin \sqrt{x}\] to make it clear
and \[u^2 = x\] is the substitution

Answer 2

Do you know integral by parts?

Answer 3

u'v+uv'?

Answer 4

In this case, you should take substitution first, and then by parts.

Answer 5

how did u conclude to that?

Answer 6

Let t = \(\sqrt x\) --> dt=\(\dfrac{1}{2\sqrt x}dx\) you have \(2\sqrt x dt=dx\) or 2tdt = dx

Answer 7

the integral becomes \( \int 2tsint dt\)
now, apply integral by parts

Answer 8

let u = 2t, dv = sint dt
you can handle from here, right?

Answer 9

yes thanx:)

Answer 10

:)

Answer 11

\[2\sin \sqrt{x}-2\sqrt{x}\cos \sqrt{x}\] is what I got which is correct also according to the book.

Answer 12

Now, how did you come to this conclusion on deciding that what should be dt and dx? alot of practice or intuition?

Answer 13

@OOOPS

Answer 14

The letter I used, t, for the first substitute is just for not confused with the second part. If I use u = sqrt x, It will be unclear on the second part when we take integral by parts. That's it.

Answer 15

okey, thanx for making it clear:)