# Evaluate the definite integral

1. May 11, 2008

### jimen113

[SOLVED] Evaluate the definite integral

1. The problem statement, all variables and given/known data
$$\int$$ Sin(3t) dt; the boundaries are Pi/3 and zero.

2. Relevant equations

3. The attempt at a solution
3-cos(pi/3)$$^{}2$$-cos(0)= not the correct answer.
Help!

Last edited: May 11, 2008
2. May 11, 2008

### lzkelley

Do a substitution: x = 3t. if you do that, then what does dt = ?
Plug x in, whats the integral of sinx?

3. May 11, 2008

### jimen113

If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?

4. May 11, 2008

### Reshma

There is no substitution required (although that would yield the same answer).
Just look at the general integration formula for Sine:
$$\int\sin nx\dx=- \frac{\cos nx}{n} + \mbox{Constant}$$
Can you get the answer now?

5. May 11, 2008

### HallsofIvy

Staff Emeritus
If x= 3t, then dx= 3dt so dt= (1/3)dx. "dt= 3" doesn't make any sense- a differential is not a number!

6. May 11, 2008

### jimen113

Thank you HallsofIvy, Reshma, & Izkelley for your help. I realized my mistake was: "dt=3"