integration by substitution!

**lawochekel** · April 6th 2012, 02:13 AM

evaluate \int\frac{\sin\sqrt{x}{\sqrt{x}dx

pls somebody should help on the equation above, confuse, thanks

**a tutor** · April 6th 2012, 02:20 AM

Did you mean $\int\frac{\sin\sqrt{x}}{\sqrt{x}}dx$ ?

use $u=\sqrt{x}$ .

Oh and put

Code:

[tex]...........[ /tex]

around your LaTeX.

**Siron** · April 6th 2012, 02:20 AM

$\int \frac{\sin\left(\sqrt{x}\right)}{\sqrt{x}}dx$
Let $\sqrt{x}=t$

**princeps** · April 6th 2012, 02:32 AM

Originally Posted by lawochekel

evaluate \int\frac{\sin\sqrt{x}{\sqrt{x}dx

pls somebody should help on the equation above, confuse, thanks

$I=\int \frac{\sin{\sqrt x}}{\sqrt x} \,dx$

$\sqrt x =t \Rightarrow \frac{1}{2\sqrt x} dx=dt \Rightarrow \frac{1}{\sqrt x} dx=2dt$

Hence :

$I=2\cdot \int \sin t\,dt=-2\cdot \cos t +C=-2\cdot \cos{\sqrt x} +C$

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