I am having trouble integrating
\begin{aligned}
\ \int_{0}^{\pi/2} x^{1/2} \cos x\, dx \end{aligned}
I see I can use the Trapezoidal or Simpson's Rule to approximate the integral, but when I used the Trapezoidal Rule, I got .6366 for n=4. I understand there should be some margin of error because I am only using 4 trapezoids, but the real answer is .7040 according to Wolfram. It seems my answer is a bit beyond what I expected - I thought I would be closer to the .7040 value.
Wolfram Link: http://www.wolframalpha.com/input/?i=integrate+sqrt%28x%29+cos+x+dx+from+0+to+pi%2F2
When I used Simpson's Rule, I got .6847 when n=4.
Edit: I resolved my own error - it was a simple button punching error (I made it for Simpon's Rule and Trapezoidal Rule - twice (I did the problem over again, too)).