Integration Question (1 Viewer)

[Bozza555]

Hi, would anyone be able to do this question for me and let me no the answer they get

For some reason the photo won't upload

Integral x^2sqrt(a^2-x^2) dx between 0 and a

 

[Carrotsticks]

Did you just want the answer, or working out?

I got:



By letting:

 

[Bozza555]

hmm i got <a href="http://www.codecogs.com/eqnedit.php?latex={}\frac{7a^{4}}{}{16}\pi" target="_blank"><img src="http://latex.codecogs.com/gif.latex?{}\frac{7a^{4}}{}{16}\pi" title="{}\frac{7a^{4}}{}{16}\pi" /></a>
must of done something wrong in the last few lines, i shall check my working thankyou!

 

[Bozza555]

I have another question aha
Could you show the working for this one though? thanks
<a href="http://www.codecogs.com/eqnedit.php?latex=\text{Show that if }I_{n}=\int_{0}^{1}\frac{dx}{(1@plus;x^{2})^{n}} \text{, then } 2nI_{n@plus;1}-(2n-1)I_{n}=\frac{1}{2^{n}}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\text{Show that if }I_{n}=\int_{0}^{1}\frac{dx}{(1+x^{2})^{n}} \text{, then } 2nI_{n+1}-(2n-1)I_{n}=\frac{1}{2^{n}}" title="\text{Show that if }I_{n}=\int_{0}^{1}\frac{dx}{(1+x^{2})^{n}} \text{, then } 2nI_{n+1}-(2n-1)I_{n}=\frac{1}{2^{n}}" /></a>

 

[Trebla]

 

[Bozza555]

thankyou !