# Integration question

• Dec 13th 2012, 11:19 PM
asilvester635
Integration question
Do I just straight up integrate (x + cosx)? and to change my interval do I plug Pi/2 and Pi/3 to cos(x)??
• Dec 13th 2012, 11:49 PM
earboth
Re: Integration question
Quote:

Originally Posted by asilvester635
Do I just straight up integrate (x + cosx)? <--- yes
and to change my interval do I plug Pi/2 and Pi/3 to cos(x)??<--- no, you have to replace x by pi/2 and pi/3 respectively

.....

Spoiler:
You should come out with
$\int_{\frac \pi3}^{\frac \pi2}(x+\cos(x)) dx = \left[\frac12 x^2 + \sin(x) \right]_{\frac \pi3}^{\frac \pi2}= \left(\frac{\pi^2}8+1\right) - \left(\frac{\pi^2}{18}+\frac12 \cdot \sqrt{3} \right)$
• Dec 13th 2012, 11:57 PM
asilvester635
Re: Integration question
awesome... so we didn't have to change the interval of Pi/2 and Pi/3, because usually that's what I'm used to doing..... So since we can't further simplify this equation we just leave it as it is??
• Dec 14th 2012, 12:48 AM
MarkFL
Re: Integration question
You only change the limits of integration if you have made a substitution. Then you write those limits in terms of the new variable.
• Dec 14th 2012, 09:41 AM
hollywood
Re: Integration question
Sometimes when I'm doing a substitution on a definite integral, I'll write $\int_{x=a}^{x=b}f(x)\ dx$ so that I remember to change the limits of integration when I do the substitution.

- Hollywood