Integral Help? :)

[OhhCalculus]

So, I've got this integral problem:

(integral from ?/6 to ?/4) sin(t)dt

Now, what I've done is:

set u=t
so du=dt
then integrate to get (-cosu)du
then I attempted to simply plug in the numbers for u
[-cos(?/4)] - [-cos(?/6)] = 0.1589186226

So, essentially, I end up with some ridiculous decimal that in no way informs me if what I'm doing is correct. I completely expected some fraction. Any input?

 

[tkhunny]

Why on earth did you perform a meaningless substitution?

Why did you breal out your calculator for pi/4 and pi/6? These are known, exact values. \(\displaystyle \left[-\cos\left(\frac{\pi}{4}\right)\right] - \left[-\cos\left(\frac{\pi}{6}\right)\right] = -\frac{\sqrt{2}}{2}\;+\;\frac{\sqrt{3}}{2}\;=\;\frac{\sqrt{3}-\sqrt{2}}{2}\)