the integral of sin sqrt of x / sqrt of x dx

Question

anonymous · Answer

This one is slightly more difficult. Have you done u-substitution?

anonymous · Answer

$$\int\limits_{}^{} \sin \sqrt{x} / \sqrt{x}$$

anonymous · Answer

hold on. i'll try, i'll post a question if anything confuses me. lol. :)

anonymous · Answer

Okay :P

anonymous · Answer

can i rewrite this as $$\int\limits_{}^{} \sin x^{1/2}/x^{1/2}$$

anonymous · Answer

Yes. What next?

anonymous · Answer

can i use power rule at sin x^1/2 then use sin rule? xD

anonymous · Answer

You have to use u-substitution. 
So let:
$$u=\sqrt{x}$$
Then the derivative of that is:
$$du=\frac{1}{2}\frac{1}{\sqrt{x}}dx$$
So replace those in your integral and get:
$$2 \int\limits \sin(u) du$$
Which is
$$-2\cos(u)+C$$
Rewrite in terms of x.
$$u=\sqrt{x} \rightarrow -2\cos(\sqrt{x})+C$$
Which is your final answer.

anonymous · Answer

wow! thank you sir! i'll try solving this to understand it further. :p

anonymous · Answer

Okay, just tell me if you get lost :P Integration is sort of my forte :P