Stuck on an Area Between Curves Question

In summary, to find the area between the curves f(x)= x^3 -9x^2 +18x and g(x)= (-x)^3 +9x^2 -18x, the points of intersection must be found (0, 3, and 6). Then, the absolute value of f(x)-g(x) must be integrated and evaluated between each point of intersection. It is important to pay attention to absolute value signs when evaluating the area between curves.
  • #1
Camronnba
5
0
I have been asked to find the area between the following curves
f(x)= x^3 -9x^2 +18x and
g(x)= (-x)^3 +9x^2 -18x

I started out by finding the points of intersection, which I found to be 0, 3, and 6. I then integrated |f(x)-g(x)|and evaluated between 6 and 0. I got an answer of zero but it says I am wrong. I then tried evaluating between 0 and 3, and 3 and 6 and adding those together, again I get zero. After that I brought out my graphing calculator, and after viewing the graphs, 0 seems like a logical answer. I must be making a mistake somewhere, if someone could please steer me in the right direction it would be greatly appreciated. Thanks
 
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  • #2
Nevermind, I should really pay attention to absolute value signs when I see them. haha
 

Related to Stuck on an Area Between Curves Question

1. What is a "Stuck on an Area Between Curves Question"?

A "Stuck on an Area Between Curves Question" is a type of problem in calculus that involves finding the area between two curves on a graph. It typically requires solving for the points of intersection between the two curves and then using integration to find the area between those points.

2. How do I approach solving a "Stuck on an Area Between Curves Question"?

To solve a "Stuck on an Area Between Curves Question," you first need to identify the two curves on the graph and find their points of intersection. Then, you can use integration to find the area between the curves by setting up a definite integral. Make sure to carefully follow the steps and check your work to ensure accuracy.

3. What are some common challenges when solving a "Stuck on an Area Between Curves Question"?

Some common challenges when solving a "Stuck on an Area Between Curves Question" include accurately finding the points of intersection between the curves, setting up the correct definite integral, and performing the integration correctly. It is important to carefully check your work and double check your calculations to avoid mistakes.

4. Can I use any integration method to solve a "Stuck on an Area Between Curves Question"?

Yes, you can use any integration method that you are comfortable with to solve a "Stuck on an Area Between Curves Question." This can include methods such as the fundamental theorem of calculus, u-substitution, or integration by parts. Choose the method that you are most confident in and that will lead to the most accurate result.

5. Are there any tips or tricks for solving a "Stuck on an Area Between Curves Question"?

One helpful tip for solving a "Stuck on an Area Between Curves Question" is to sketch the two curves on a graph to visualize the problem. This can help you identify the points of intersection and get a better understanding of the area you are trying to find. It is also important to carefully label your work and show all steps clearly to avoid errors.

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