Evaluate the definite integral

[jimen113]

[SOLVED] Evaluate the definite integral

1. Homework Statement
$$\int$$ Sin(3t) dt; the boundaries are Pi/3 and zero.

Homework Equations

The Attempt at a Solution

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

 

[lzkelley]

Do a substitution: x = 3t. if you do that, then what does dt = ?
Plug x in, what's the integral of sinx?

 

[jimen113]

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

 

[Reshma]

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

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?

 

[HallsofIvy]

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

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

 

[jimen113]

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