Finding the area between 3 functions

In summary, the individual is struggling with a math problem involving finding the area of a region enclosed by three curves. They have plotted the graph and found the intersection points, but are unsure of whether to integrate with respect to x or y. They have attempted to integrate with respect to x, but are getting the wrong answer. After realizing their mistake of not dividing 7 by 2, they are able to solve the problem and thank ehildahh for their help.
  • #1
lilypeach
6
0
Hi all, I've been attempting this problem for hours and I believe I am using the correct method, but I keep on getting the wrong answer, ANY help as to what I am doing wrong is greatly appreciated.

The question is:

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
2y = 3sqrt(x) , y = 5, and 2y + 4x = 7

I've plotted the graph, and found the intersection points, with are : x= -3/4 , x=1 x= 11.11111

I integrated with respect to X (I know that y would be easier, but I'm not too sure how to do that yet), therefore, the areas were:

step 1: int. between -3/4 to 1 with the function to be integrate being : 5-(-2x+7) and

step 2: int. between 1 to 11.11111111 with the function to be integrated being : 5-([3sqrt(x)]/2)

I integrated step 1 (2x-2, integrate that, and I got x^2-2x), when plugging in the numbers, I got -3.0625

I integrated step 2, and got 5x-x^3/2, when plugging in the numbers, I got 14.51851852

I added both areas and got 11.45601.

What am I doing wrong?..
 
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  • #2
lilypeach said:
2y = 3sqrt(x) , y = 5, and 2y + 4x = 7
...
step 1: int. between -3/4 to 1 with the function to be integrate being : 5-(-2x+7) and

Divide 7 by two, too.

ehild
 
  • #3
ahh, I can't believe I missed that. :X! thanks a million ehild
 

FAQ: Finding the area between 3 functions

What is the purpose of finding the area between 3 functions?

Finding the area between 3 functions is a mathematical process used to determine the total area that is enclosed by three different functions on a graph. This can be useful in various scientific fields, such as physics and engineering, to calculate the volume of a 3-dimensional shape or to analyze the behavior of a system.

How is the area between 3 functions calculated?

To calculate the area between 3 functions, you will need to first graph the three functions and determine the points where they intersect. Then, you can break down the enclosed area into smaller, simpler shapes (such as rectangles or triangles) and use basic area formulas to find the area of each shape. Finally, you can add up all the areas of the smaller shapes to get the total area between the three functions.

Can the area between 3 functions be negative?

Yes, the area between 3 functions can be negative if the three functions intersect in a way that creates an enclosed area below the x-axis. In this case, the area would be considered negative because it is below the x-axis, which is often used as the baseline for calculating area.

What are some real-world applications of finding the area between 3 functions?

Finding the area between 3 functions has many real-world applications, such as calculating the volume of a 3-dimensional shape, determining the amount of liquid in a container with a curved bottom, and analyzing the behavior of complex systems in physics and engineering. It can also be used in economics and finance to calculate the area under a demand curve.

Is there a specific formula for finding the area between 3 functions?

There is no specific formula for finding the area between 3 functions, as it depends on the specific functions and their intersections. However, there are general methods and techniques, such as breaking down the area into smaller shapes and using basic area formulas, that can be applied to find the area between any three functions.

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