Single integral integration of a difficult integrand

[M98Ranger]

I was wondering if any one could give me an idea of how to integrate the following function.

\(\displaystyle \[
\delta *\int_0^{2\pi } {\sqrt {8Cost + 9t^2 } } dt
\]\)

 

[pka]

I find no elementry closed form.
You can try this site: http://integrals.wolfram.com/index.jsp

 

[tkhunny]

I'm guessing the \(\displaystyle 9t^{2}\) is NOT in the cosine argument, but you probably should write it so it is more obvious.

 

[galactus]

Try a Riemann sum, say, the midpoint rule. Of course, the more

subintervals the more accurate. If you have to do it the long way, n=10 isn't too bad.

With 10 subintervals, I get 60.26744143

The actual is 60.31622502

 

[M98Ranger]

You guys are awsome!....Sorry it wasn't written very well, I should have proofed it. My bad. Thanks for all your help. Time to hit the books for one last evening before I take my Strengths of Materials test. You guys are seriously a great asset! Thanks for all your hard work and thought!! I will remember the rieman thing next time.