What is the area between 3 equations with e^(5x), e^(9x), and x=1?

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In summary, the area between three equations refers to the region enclosed by three curves or lines on a graph. It can be calculated using the method of integration, by finding points of intersection and setting up and solving integrals for each region. The area can be negative if the curves intersect in a specific way, and there are various real-world applications for this concept. The method for finding the area between three equations is similar to that of finding the area between two equations, but may require more complex mathematical techniques.
  • #1
mshiddensecret
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Homework Statement



Sketch the region enclosed by y=e^(5x), y=e^(9x), and x=1. Decide whether to integrate with respect to x or y. Then find the area of the region.

Homework Equations





The Attempt at a Solution



I tried graphing all the lines but they the e^(9x) line never seem to reach x=1 so they don't all intersect.
 
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  • #2
Surely you know that e^(9*1)= e^9? That's a very large number (larger than 8000) but is still finite! The area of the region is [itex]\int_0^1 (e^{9x}- e^{5x})d[/itex].
 
  • #3
Thanks! I got it. Its 870.7489
 

1. What is the area between three equations?

The area between three equations refers to the region enclosed by three curves or lines on a graph. It can also be thought of as the space bounded by these three equations.

2. How do you calculate the area between three equations?

The area between three equations can be calculated using the method of integration. First, find the points of intersection between the three curves. Then, set up and solve an integral for each region between the curves. Finally, add up the individual areas to get the total area between the three equations.

3. Can the area between three equations be negative?

Yes, the area between three equations can be negative if the curves intersect in a way that creates a region below the x-axis. This indicates that the area is bounded by the three equations in a clockwise direction.

4. Are there any real-world applications of finding the area between three equations?

Yes, finding the area between three equations has various real-world applications, such as calculating the volume of a solid with irregular cross-sections, determining the area of overlap between different fields of study, and estimating the amount of land needed for different agricultural crops.

5. Is there a specific method for finding the area between three equations?

Yes, the method for finding the area between three equations is similar to the method for finding the area between two equations. However, in this case, the number of integrals and regions may be greater, and it may require more complex mathematical techniques, such as u-substitution or integration by parts.

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