Homework Help: Simple integration but i forgot how to do it!

1. Oct 2, 2005

mr_coffee

Here is my work and problem:

i made an sign mistake, d/dt (cos t) = -sin(t).http://img101.imageshack.us/img101/561/blah4gk.jpg [Broken]

Last edited by a moderator: May 2, 2017
2. Oct 2, 2005

Fermat

There's a problem with the link.

3. Oct 2, 2005

mr_coffee

Ahh sorry!!
http://img101.imageshack.us/img101/561/blah4gk.jpg [Broken]

Last edited by a moderator: May 2, 2017
4. Oct 2, 2005

TD

That seems correct, what's the problem? You only forgot the unit vector j I believe.

5. Oct 2, 2005

mr_coffee

oh sorry, i got that answer from someone, but didn't know how they got it! the parts i were i let u = cos (PI t);
du = -PIsin(PI t);
-1/PI de = sin(PI t);
but i don't know how that helps me when i plug it back in!

6. Oct 2, 2005

TD

Just integrate each component. Pi is just a constant, you don't even need a real substitution for it. Do it indirectly by adjusting the dt and correcting in front of the integral.

$$\int {\cos \left( {\pi t} \right)dt} = \frac{1} {\pi }\int {\cos \left( {\pi t} \right)d\left( {\pi t} \right)} = \frac{{\sin \left( {\pi t} \right)}} {\pi } + C$$

7. Oct 2, 2005

mr_coffee

OHh!! i was making that way more complicated then it should havve been! thanks again TD! :D

8. Oct 3, 2005

No problem