cos(sqrt x)

• August 3rd 2009, 06:08 AM
cos(sqrt x)
HELLO,

I d be grateful to anyone who solves the following, as I have been trying for ages but it is not working.

Q/ solve by finding appropriate substitution and then integrate by parts:
integral of cos(sqrt x).

Thanks.
• August 3rd 2009, 06:22 AM
CaptainBlack
Quote:

HELLO,

I d be grateful to anyone who solves the following, as I have been trying for ages but it is not working.

Q/ solve by finding appropriate substitution and then integrate by parts:
integral of cos(sqrt x).

Thanks.

What is wrong with $u=\sqrt{x}$, then integrate by parts

CB
• August 3rd 2009, 06:29 AM
I am sorry but could you make it a little clearer.
Thanks.
• August 3rd 2009, 06:37 AM
CaptainBlack
Quote:

I am sorry but could you make it a little clearer.
Thanks.

If $u=\sqrt{x}$ we have:

$
\int \cos(\sqrt{x})\; dx=\int \cos(u) \frac{dx}{du}\;du=2 \int u\cos(u)\;du
$

and now you use integration by parts.

(If you need more help WolframAlpha will give you a step by step explanation of the complete process)

CB
• August 3rd 2009, 06:45 AM