Help!!!!
How do I integrate this:
integral (2x)/(sqrt1-x^2) from 0 to 1/2

Question

Help!!!!
How do I integrate this:
integral (2x)/(sqrt1-x^2) from 0 to 1/2

anonymous · Answer

$$\int\limits_{0}^{1/2}2x/\sqrt{1-x^2}    dx$$

anonymous · Answer

try $u=1-x^2$

anonymous · Answer

$$\int\limits_{0}^{\frac{ 1 }{ 2 }}\frac{ 2x }{ \sqrt{1-x^2} }dx$$
put $$x^2=t,2 x dx=dt$$
when x=0,t=o
$$when~ x=\frac{ 1 }{ 2 },t=\frac{ 1 }{ 4 }$$
can you proceed further?

anonymous · Answer

no I have no idea how to do this

anonymous · Answer

you write the following:
"let $u=1-x^2$ and so $du=-2xdx$

anonymous · Answer

then take your integral and replace $1-x^2$ by $u$  and replace the $2xdx$ by $-du$ 
pull the minus sign out front

anonymous · Answer

that gives you 
$$-\int \frac{du}{\sqrt{u}}$$

anonymous · Answer

now find the anti derivative by writing this in exponential form and using the power rule backwards