Question

trig sub question

Answer 1

\[\int\limits_{0}^{3}x^{2}\sqrt{25-x^{2}}\]

Answer 2

so I had sintheta=x/5 and so dx=5sinthetadtheta and sqrt(25-x^2)=5costheta

Answer 3

\[\int\limits25\sin^{2}\theta 5\cos \theta 5 \cos \theta d \theta \]

Answer 4

I used th\[\frac{ 625 }{ 8 } \int\limits 1-\cos2 \theta d \theta \]e double angle identity and then pythagorean then double angle again to get

Answer 5

integrating and subing back in x I got \[\frac{ 625 }{ 8 }[\arcsin(x/5)-\frac{ x \sqrt{25-x^{2}} }{ 25 }]\]

Answer 6

I plugged the original integral into wolfram alpha though and did not get that

Answer 7

http://www.wolframalpha.com/input/?i=integral+0+to+3+x%5E2sqrt%2825-x%5E2%29

Answer 8

@ganeshie8

Answer 9

see if this helps

Answer 10

thank you I got where I messed up