# Help with some intergration

• Nov 27th 2008, 11:04 AM
rpatel
Help with some intergration
Hello

I need help with these 3 intergrations questions please

thanks

Kind Regards
• Nov 27th 2008, 01:11 PM
Mathstud28
Quote:

Originally Posted by rpatel
Hello

I need help with these 3 intergrations questions please

thanks

Kind Regards

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 PM
Chris L T521
Quote:

Originally Posted by Mathstud28
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.

....or you could have made the simple substitution $\displaystyle z=x-x^2$ which would convert the integral into $\displaystyle -\int z^{-\frac{1}{2}}\,dz$.
• Nov 27th 2008, 01:53 PM
Mathstud28
Quote:

Originally Posted by Chris L T521
....or you could have made the simple substitution $\displaystyle z=x-x^2$ which would convert the integral into $\displaystyle -\int z^{-\frac{1}{2}}\,dz$.

....nu uh....(Rofl)