# Homework Help: How to integrate this?

1. Oct 3, 2008

### kingwinner

1. The problem statement, all variables and given/known data
n
∫2n-tdt
0

2. Relevant equations
N/A

3. The attempt at a solution
I've been wondering about the correct way to deal with this type of integral for quite a long time. To me, the above integral looks like something of the form:
n
∫f(n,t)dt
0
n appears in the integrand AND in the limits of integration, how can I integrate in this case?

I am just wondering whether n can be treated as a "constant" in the above integral, i.e. can I treat 2^n as a constant and pull the 2^n OUT of the integral and evaluate
n
∫2-tdt ?
0

Thank you for explaining!

2. Oct 3, 2008

### morphism

Yes, the n is a constant in this case.

3. Oct 3, 2008

### HallsofIvy

First, 2n-t= 2n 2-t.

Second, the derivative of 2t is (ln 2)2t so the anti-derivative is 2t/ln(2).

4. Oct 3, 2008

### kingwinner

So even though "n" appears in the integrand and also appears in the limits of integration, we can still treat the "n" in the integrand as a constant and use the property ∫cf(t)dt=c∫f(t)dt ?

Last edited: Oct 3, 2008
5. Oct 3, 2008

### Defennder

If you integrating with respect to t, you don't have to worry about anything else unless n is a function of t, which it is not stated to be.