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.