Integral of pythagorean type formula? 1

[kilkenny]

Can anyone integrate this?

Integral(sqrt[((cosx)^2)+(x^2)]dx

It is like the integral of a pythagorean formula composed of 2 functions of x.

Thanks,

kilkenny

 

[ivymike]

The tool at

http://www.integrals.com/index.en.cgi

can't seem to do it.

Are you sure that the equation is written correctly?

If you need the value of the integral over a specific range, try integrating numerically (using excel or similar).

 

[kilkenny]

Yes there was a right bracket missing. Here is the equation again:

Integral(sqrt[((cosx)^2)+(x^2)]dx

I'll use numerical integration but I was wondering if anyone out there knew of a definite integral for this one.

Kilkenny

 

[Sparweb]

MathCAD wouldn't crack it, either.

MathCAD can, however, evaluate it for any range, and it seems to give real numbers for any real number input.

Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout

 

[Denial]

And (my early version of) "Derive" cannot do it either.

 

[IRstuff]

[sqrt(x)]^3/3 + 1/3[cos(sqrt(x^3))^2]

from

http://www.integrals.com/index.en.cgi

TTFN

 

[Denial]

I could not get that site to give any answer. It just quoted my integral back to me, which I take to mean "no can do".

 

[corus]

The site worked for me after the expression cosx was input correctly, ie. cos(x), and the minimum number of brackets was used.

corus

 

[Rich2001]

Make the substitution 1/2[(exp(ix) + exp(-ix)] for cos(x)
once you do this MathCad and Dervive can solve.

 

[Cockroach]

I've tried it various ways using classical methods of calculus, but each have failed because of the implicit function of "x" to "cos x". At one point, I thought it would reduce to an Elliptic Integral, but even this cratered in the end.

I think numerical methods is your best bet, which is probably what many of readers have suggested using canned software programs.

I'm going to keep at it, I like the abuse. Hopefully I can prove the answer in my own lifetime!

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[arto]

If you have to use calculus, you're doing something wrong..... ;-)