Integrate sqrt(x - x^2)
I've been struggling with this question for hours but has come no closer to solving it. I know it involes the sin inverse function but I cant find a suitable substitution to make that happen.
Would appreciate any help
Integrate sqrt(x - x^2)
I've been struggling with this question for hours but has come no closer to solving it. I know it involes the sin inverse function but I cant find a suitable substitution to make that happen.
Would appreciate any help
As with most of these, there are various ways to go about it.
$\displaystyle \int\sqrt{x-x^{2}}dx$
$\displaystyle \int\sqrt{x(1-x)}dx$
Make the sub $\displaystyle x=\frac{2u+1}{2}, \;\ dx=du$
and we get $\displaystyle \frac{1}{2}\int\sqrt{1-4u^{2}}du$
Now, there are many routes to take, but a trig sub may be OK.
Can you do it from here?.