Sketch the region enclosed by the given curves. Decide whether to integrate.

In summary, when tasked with finding the area between given curves, it is important to first sketch the region and determine whether to integrate with respect to x or y. A typical approximating rectangle can then be drawn and its height and width labeled. After integrating, the resulting area should always be a positive value. If the result is negative, it is an indication that a mistake may have been made and the answer should be checked. To determine which of the two curves, f(x) or g(x), should be subtracted from the other when integrating, one can refer to the graph. With this approach, the resulting area will always be accurate and positive.
  • #1
phillyolly
157
0

Homework Statement


Sketch the region enclosed by the given curves. Decide
whether to integrate with respect to x or y. Draw a typical approximating
rectangle and label its height and width. Then find the
area of the region.

Homework Equations


The Attempt at a Solution


My result gave me an answer "-20". The area cannot be negative, please check my answer for a mistake?
 

Attachments

  • answer.jpg
    answer.jpg
    19.5 KB · Views: 425
Physics news on Phys.org
  • #2
If you want to find the area between two curves f(x) and g(x), how do you know whether to integrate f(x)-g(x) or g(x)-f(x)? Use your graph.
 
  • #3
OK, I got it. This is my try. Thank you.
 

Attachments

  • answer.jpg
    answer.jpg
    28.5 KB · Views: 423
  • #4
Yes, that's right.
 

1. What is the purpose of sketching the region enclosed by given curves?

The purpose of sketching the region enclosed by given curves is to visually represent the boundaries of the region and understand its shape and size. This helps in determining the limits of integration when finding the area or volume of the region.

2. How do I decide whether to integrate when sketching the region enclosed by curves?

In order to decide whether to integrate, you must first determine if the region is bounded by a function or by multiple functions. If the region is bounded by a single function, you can use integration to find the area under the curve. If the region is bounded by multiple functions, you will need to use integration to find the area between the curves.

3. What information do I need to sketch the region enclosed by curves?

You will need to know the equations of the curves, the intervals of integration, and any points of intersection between the curves. You may also need to know the orientation of the curves (above or below the x-axis) in order to accurately sketch the region.

4. What is the process for sketching the region enclosed by curves?

The process for sketching the region enclosed by curves involves plotting the equations on a coordinate plane, identifying the boundaries of the region, and shading in the area between the curves. You may also need to label any points of intersection or important features of the region.

5. How can I check if my sketch of the region enclosed by curves is correct?

You can check the accuracy of your sketch by using the equations of the curves to find the area of the region or by using a graphing calculator to plot the equations and compare your sketch to the graph. Additionally, you can check if your sketch follows the rules of integration, such as the area under a curve always being positive.

Similar threads

Replies
3
Views
7K
  • Calculus and Beyond Homework Help
Replies
15
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
5K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
666
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top