# Evaluate the definite integral

[SOLVED] Evaluate the definite integral

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

## The Attempt at a Solution

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

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

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

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