# Math Help - Integrating sin(pi*t)

1. ## Integrating sin(pi*t)

I'm doing a differential equation problem, kind of confused on a simple integration of sin(pi*t)... which supposedly equals (1/pi)sin(pi*t) + c

The problem was...
y/t^2 = INT(cos(pi*t))dt

Why is it 1/pi?

2. Originally Posted by pakman
I'm doing a differential equation problem, kind of confused on a simple integration of sin(pi*t)... which supposedly equals (1/pi)sin(pi*t) + c

The problem was...
y/t^2 = INT(cos(pi*t))dt

Why is it 1/pi?
What is integral,
INT cos (2x) dx = 1/2 * sin (2x) +C

What about,

INT cos (3x) dx = 1/3*sin(3x) +C

...

In general if k!=0 then,
INT cos(kx) dx = 1/k*sin (kx)+C

Use the substitution t=kx.

3. If you can express your phone number as a sum of four squares, wouldn't that imply you knew your own phone number?

4. Originally Posted by AfterShock
If you can express your phone number as a sum of four squares, wouldn't that imply you knew your own phone number?
Ah! But not by Lagrange's 4 Square theorem. Or Fermat's Polygonal Number Theorem.