# Homework Help: Finding the area of the region

1. Feb 25, 2005

find the area of the region

$$y=e^{4x}$$
$$y=e^{6x}$$

first thing i did was set them equal to each other and multiply by $$ln$$ which got me 4x=6x, that's where i got stuck. how would i find the x-intercepts?

2. Feb 25, 2005

### vincentchan

what do you mean? what area? function doesn't have area.....

EDIT:
These two function intersect at 1 point (0,1) only...

Last edited: Feb 25, 2005
3. Feb 25, 2005

### maverick280857

1. You can't multiply by $ln$. Its an operator.
2. The exponential function is strictly increasing over the whole real line. There's no way it takes the same value twice (unless its of the form e^{periodic function} which it isn't in your case).
3. Drawing proper graphs for both functions referred to the same set of orthogonal axes might help. How fast do the functions grow?

Last edited: Feb 25, 2005
4. Feb 25, 2005

### Elendil

$$Area = \int_{x_1}^{x_2} ( e^{6x} - e^{4x} ) \delta x$$
where $$x_1$$ and $$x_2$$ should found from
$$e^{4x} = e^{6x}$$

Last edited: Feb 26, 2005
5. Feb 25, 2005

### HallsofIvy

Assuming you mean "the area of the region between the graphs of" e4x and e6x, you are going to need at least one more boundary. Those two graphs cross, of course, at x= 0, y= 1 but not at any other point. Those two graphs do not define a region.