Problem regarding Integrating using trigonometric substitution.

[AzulSeca]

integral x^2 / sqrt(7-x^2)

I cant get the right anwer!

orange markings are one solution i tried by making sin = u

blue was another solution i tried where i use an identity for the derivative of sin^2 theta

 

[renegade05]

A detailed solution can be found here:

http://www.wolframalpha.com/input/?i=integrate+x%5E2%2F%287-x%5E2%29%5E%281%2F2%29


You had the right idea when you let \(\displaystyle x=\sqrt{7}sin(u)\).

See where you went wrong by following the link. If you are still having troubles, reply back!

 

[HallsofIvy]

You are good up through \(\displaystyle 7\int sin^2(\theta)d\theta\)- except that you did not write the "\(\displaystyle d\theta\)" and that may be what threw you off. You indicate that you want to use the substitution \(\displaystyle sin(\theta)= u\) so that \(\displaystyle sin^2(\theta)= u^2\). But then you must also have \(\displaystyle cos(\theta)d\theta= du\)- and you cannot do that because you do not have "\(\displaystyle cos(\theta)\)" in the integral.


Instead, the standard way of integrating an even power of sine or cosine is to use the trig identities \(\displaystyle sin^2(\theta)= \frac{1}{2}(1- cos(2\theta))\) and \(\displaystyle cos^2(\theta)= \frac{1}{2}(1+ cos(2\theta))\).

 

[AzulSeca]

OK i see my error, thanks guys