How to find the new limits of integration

In summary, When rotating using the washer method about the x-axis, the new limits of integration can be found by setting y=0 and y=9-x2 and solving for x, where x represents the original limits of integration. This applies for both the shell and washer methods. It is also important to note that the new limits will vary depending on the given function and axis of rotation.
  • #1
firekid123
8
0

Homework Statement



I'm confused about a certain aspect of shell method, washer method, and disk method. If I want to rotate using the washer method about the x-axis how do I get the new limits of integration?

For example: y = 9-x2 over [0,3] about x-axis.
I solved for x and got: x = sqrt(9-y) but how do I calculate the new limits?
Also do I need to find the new limits for disk, shell, and washer method in certain cases or is it only for shell and washer?

I know how to set up and solve the integral it's just calculating the new limits. Any help would be great.
 
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  • #2
You are initially given values for x, so when x=0 what is y? Similarly when x=3 what is y?

(from the equation y=9-x2)

Those will be your limits.
 

Related to How to find the new limits of integration

1. How do I determine the new limits of integration?

To find the new limits of integration, you first need to identify the new region of integration. This can be done by visualizing the area or by using equations to describe the boundaries of the region. Once you have determined the new region, you can then set up the new limits of integration by finding the minimum and maximum values for each variable within the region.

2. What are the steps to finding the new limits of integration?

The first step is to identify the new region of integration. Then, determine the minimum and maximum values for each variable within the region. Next, substitute these values into the original integral. Finally, evaluate the integral to find the new limits of integration.

3. Can I use geometry to find the new limits of integration?

Yes, geometry can be a useful tool in finding the new limits of integration. By visualizing the region of integration, you can identify the boundaries and determine the minimum and maximum values for each variable within the region.

4. Is there a specific formula for finding the new limits of integration?

No, there is not a specific formula for finding the new limits of integration. It requires understanding the given region of integration and using mathematical techniques to determine the new limits.

5. Are there any special cases when it comes to finding the new limits of integration?

Yes, there are some special cases that may require additional steps to find the new limits of integration. One example is when the region of integration is rotated, which may require using trigonometric functions to determine the new limits.

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