# evaluate the definite integral

• Dec 3rd 2012, 10:38 AM
asilvester635
evaluate the definite integral
so at the very end when i integrated (2t + cost) i got (t^2 + sint)..... then i plugged in positive and negative Pi/2...
in which i got [(Pi/2)^2 + sin(Pi/2) - (-Pi/2)^2 + sin(-Pi/2)]......

then i got [((Pi^2/4) + 1) - (-Pi^2/4) + -1]..... IS THAT RIGHT?
• Dec 3rd 2012, 10:43 AM
Scopur
Re: evaluate the definite integral
• Dec 3rd 2012, 01:32 PM
Re: evaluate the definite integral
Well you're supposed to get 2 as your evaluated integral from -pi/2 to pi/2 and what you have looks like 2pi^2/4+2. When you squared the negative pi/2 the negative goes away and you're left with pi^2/4 so you can cancel out with pi^2/4 .
• Dec 3rd 2012, 01:52 PM
MarkFL
Re: evaluate the definite integral
You could write:

$2\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}t\,dt+\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\cos(t)\,dt$

Using the odd function rule on the first integral, and the even function rule on the second we have:

$2\cdot0+2\int_{0}^{\frac{\pi}{2}}\cos(t)\,dt=2 \left[\sin(t) \right]_{0}^{\frac{\pi}{2}}=2\left(\sin\left(\frac{\pi}{2 } \right)-\sin(0) \right)=2(1-0)=2$
• Dec 7th 2012, 10:24 AM
asilvester635
Re: evaluate the definite integral
so you plugged in -Pi/2 into cos(t) thats why you got 0? well why didn't you do the same thing for the positive Pi/2???
• Dec 7th 2012, 10:56 AM
asilvester635
Re: evaluate the definite integral
so you plugged in -Pi/2 into cos(t) thats why you got 0? well why didn't you do the same thing for the positive Pi/2??????
• Dec 7th 2012, 11:34 AM
topsquark
Re: evaluate the definite integral
Quote:

Originally Posted by asilvester635
[((Pi^2/4) + 1) - (-Pi^2/4) + -1]..... IS THAT RIGHT?

Actually, line 2 is incorrect. You need to watch your signs more carefully: It should be
[(Pi/2)^2 + sin(Pi/2)] - [(-Pi/2)^2 + sin(-Pi/2)]

Pi^2/4 + 1 - Pi^2/4 + 1

-Dan

Geez! A lot of posts were made while I wrote that!
• Dec 7th 2012, 12:15 PM
asilvester635
Re: evaluate the definite integral
why did the exponent turn into 2/4?? what did you do with it?
• Dec 7th 2012, 01:26 PM
HallsofIvy
Re: evaluate the definite integral
It didn't. If the exponent were 2/4, it would be written pi^(2/4) or pi^(1/2). pi^2/4 means (pi^2)/4.