How Do You Find the Area Between Intersecting Graphs?

[ProBasket]

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?

 

[vincentchan]

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


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

 

[maverick280857]

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?

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?

 

[Elendil]

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?

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}

 

[HallsofIvy]

Assuming you mean "the area of the region between the graphs of" e^4x and e^6x, 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.