Hello

I need help with these 3 intergrations questions please

thanks

Kind Regards

Printable View

- Nov 27th 2008, 11:04 AMrpatelHelp with some intergration
Hello

I need help with these 3 intergrations questions please

thanks

Kind Regards - Nov 27th 2008, 01:11 PMMathstud28
1. $\displaystyle \begin{aligned}\frac{2x-1}{\sqrt{x-x^2}}&=\frac{2x-1}{\sqrt{\frac{1}{4}(1-(1-4x+4x^2))}}\\

&=\frac{2x-1}{\sqrt{\tfrac{1}{4}(1-(1-2x)^2}}\\

&=\frac{2x-1}{\tfrac{1}{2}\sqrt{1-(1-2x)^2}}\\

&=2\frac{2x-1}{\sqrt{1-(2x-1)^2}}\end{aligned}$

Now just let $\displaystyle \varphi=2x-1$ and see the next problem.

2. $\displaystyle \int\frac{dx}{\sqrt{1-x^2}}$

Let $\displaystyle \sin(\theta)=x$

3. $\displaystyle \int\arcsin(x)dx$

Let $\displaystyle \arcsin(x)=\varphi$ - Nov 27th 2008, 01:52 PMChris L T521
- Nov 27th 2008, 01:53 PMMathstud28