Area between 2 curves, just need someone to check my work.

In summary, the area between 2 curves refers to the enclosed region between two curves on a graph. It can be found by calculating the definite integral of the difference function between the two curves. To find this area, you can graph the curves, find the difference between them, set up a definite integral, use the points of intersection as limits, and solve the integral. This area can be negative if one curve is above the other in certain regions, and it will be equal to 0 if the curves do not intersect. The area between 2 curves can be found using calculus, but there are also other methods available.
  • #1
Kuma
134
0

Homework Statement


Alright so the problem:

Find the reigon in the xy plane that is bounded by the curves:

x = y^2
and
2y + x = 3


quickly solving for the y coordinates of intersection, i get
y = -3 and 1

so using horizontal components i got:

[tex]\int^{1}_{-3}[/tex] 3-2y - y^2

and then integrating and quickly solving i get 32/3 as a final answer
do the steps seem alright or have i made a mistake somewhere?

Many thanks :)
 
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  • #2
That's right.
 

FAQ: Area between 2 curves, just need someone to check my work.

What is the "area between 2 curves"?

The "area between 2 curves" refers to the region enclosed by two curves on a graph, typically on the x-y plane. This area can be calculated by finding the definite integral of the function that represents the difference between the two curves.

How do I find the area between 2 curves?

To find the area between 2 curves, you can follow these steps:

  1. Graph the two curves and identify the points of intersection.
  2. Find the difference between the two curves by subtracting one function from the other.
  3. Set up the definite integral by using the difference function and integrating with respect to x or y, depending on the orientation of the curves.
  4. Use the points of intersection as the limits of integration.
  5. Solve the integral to find the area between the two curves.

Can the area between 2 curves be negative?

Yes, it is possible for the area between 2 curves to be negative. This can occur when the two curves intersect and one curve is above the other in certain regions. In this case, the integral will result in a negative value, indicating that the area between the two curves is negative.

What if the curves do not intersect?

If the curves do not intersect, then there is no enclosed region and therefore no area between them. In this case, the area between 2 curves would be equal to 0.

Can I find the area between 2 curves using calculus?

Yes, the area between 2 curves can be found using calculus. This is typically done by setting up a definite integral and evaluating it using the fundamental theorem of calculus. However, there are other methods for finding this area, such as using geometric formulas or numerical integration techniques.

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