Finding areas between graphs

In summary, to find the exact area between y=ex, y=2, and the y axis, you need to sketch the region and find the intersection of y=ex and y=2. Then, determine the typical area element and limits of integration. Simply integrating from 0 to 2 will not give the correct answer. This problem may require some additional steps and calculations.
  • #1
apiwowar
96
0
find the exact area between y=ex, y=2, and the y axis

im not looking for a solution, just hints on how to get started.
would i just go ahead and integrate the function from 0 to 2 or would i solve the function for x and then integrate or are those 2 idea just completely wrong?

thanks
 
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  • #2
apiwowar said:
find the exact area between y=ex, y=2, and the y axis

im not looking for a solution, just hints on how to get started.
would i just go ahead and integrate the function from 0 to 2 or would i solve the function for x and then integrate or are those 2 idea just completely wrong?

thanks
Step 1 is to sketch the region whose area you want to find. Then find where y = ex intersects y = 2. After you have done that, you need to find the typical area element (either horizontal or vertical) and the limits of integration (which are NOT 0 and 2). There is a bit more to this problem than simply "integrat[ing] the function from 0 to 2."
 
  • #3
mark is right. you are looking for an area near 1.
 
  • #4
yea that makes sense now, its just been a while since I've done these
 

1. What is the purpose of finding areas between graphs?

The purpose of finding areas between graphs is to calculate the total area of two or more intersecting graphs. This can provide important information about the relationship between the graphs and can be used to solve various real-world problems in fields such as physics, economics, and engineering.

2. How do you calculate the area between two graphs?

To calculate the area between two graphs, you first need to identify the points of intersection between the two graphs. Then, you can use basic integration techniques to find the definite integral of the difference between the two functions over the interval of intersection. The resulting value will be the area between the two graphs.

3. Can the area between two graphs be negative?

Yes, the area between two graphs can be negative. This can occur when the graph of one function is below the graph of another function in certain regions. In this case, the area between the two graphs will be negative, indicating that the second function occupies more space than the first function.

4. What are some real-world applications of finding areas between graphs?

Finding areas between graphs has many real-world applications, such as calculating the displacement of an object over time, determining the total revenue and cost of a business, and calculating the total work done by a force over a given distance. It can also be used to analyze changes in population growth, analyze stock market trends, and optimize the production of goods in manufacturing.

5. Are there any limitations to finding areas between graphs?

There are some limitations to finding areas between graphs. The accuracy of the calculated area depends on the accuracy of the data used to create the graphs. Additionally, finding the area between two complex or irregularly shaped graphs can be challenging and may require advanced mathematical techniques. It is also important to note that finding the area between two graphs does not provide information about the rate of change of the functions, as it only calculates the total difference between them.

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