Question

evaluate the integral.

x^3(sqrt(5-x^2))

Answer 1

yes it is trig substitution....i think i just figure out how to do it

Answer 2

I mean \(x=\sqrt{5}\sec(\theta)\)

Answer 3

So what you get is:\[\large \sqrt{5^3}\sec^3(\theta)\sqrt{5-5\sec^2(\theta)}\]

Answer 4

\[\large \sqrt{5^3}\sec^3(\theta)\sqrt{5(1-\sec^2(\theta))}\]\[\large \sqrt{5^3}\sec^3(\theta)\sqrt{5\tan^2(\theta)}\]

Answer 5

Which simplifies more into:\[25sec^3(\theta)|\tan(\theta)|\]

Answer 6

Since \[\frac{d}{dx}\sec(x)=\sec(x)\tan(x)\]We can substitute even further...\(u=\sec(\theta)\)

Answer 7

Wait... have I messed up somewhere yet...

Answer 8

Yeah I did... definitely should have used \(\sin\) instead of \(\sec\)

Answer 9

Thats what I also did but with sin.

Answer 10

Ok. i think i know how to do this. :D