# integration question

Discussion in 'Mathematics' started by fudgesweets, Mar 2, 2011.

1. ### fudgesweetsNew commenter

How would you integrate 4*sqrt(1+3(cosx)^2)......any ideas for a substitution? perhaps?

2. ### fudgesweetsNew commenter

How would you integrate 4*sqrt(1+3(cosx)^2)......any ideas for a substitution? perhaps?

3. ### DMNew commenter

Where does the question come from? I think it is an elliptical integral of the second kind.

6. ### DMNew commenter

I used an invention that predates WA Casy ... my eyes.

Ouch.

8. ### David GetlingSenior commenter

I'd also like to know where this came from, as I had a good play with this and didn't get anywhere. Like DM, my first thought was elliptical. If this really was in an A-level exam I'd imagine there were limits given, with the expectation of using a numerical method: in which case the OP should have said so.

9. ### numcrunch

quick estimate 2*cos(2*x)+6 , integrates to sin(2*x) + 6*x.
also try fourier series ,
even function !, so limits -a,a integrates to zero.
all b(n) coefficients zero apparently
a0 + a1*cos(?) + a2*cos(?) +
approximate function then integrate term by term perhaps.

10. ### Colleen_YoungOccasional commenter

DM - I do know you can integrate stuff (so can I), your wording amused me for some reason when I read it, reminded me of WolframAlpha which is one seriously useful resource.
It even has Polecat's 19.4 (well, 19.3769 approx, more digits if you want)
WolframAlpha

11. ### Polecat

I used Maple rather than Mathematica - personal preference.
If I have the time, I might see what sort of accuracy Simpson's
rule produces with not too many ordinates.