# Need help setting up integral. (Doesn't have to be solved)

• Ashford
In summary, the conversation discusses setting up a definite integral to find the volume of a solid generated by revolving the region enclosed by the curves y=(x^2)-1, x=2, and y=0 about the y-axis. The person has looked for help in their book but is still stuck. They have attempted to graph the problem and have set up an integral with limits of 0 and 2, but are unsure if it is correct. They are also unsure of whether to use shells or disks to find the volume and what expression represents the volume element.
Ashford

## Homework Statement

Set up a definite integral that could be evaluated to find the volume of the solid that results when the region enclosed by the curves y=(x^2)-1, x=2, and y=0 is revolved about the y-axis.
(doesn't have to be solved) I have look at my book for help and I'm stuck.

What have you tried so far?

Please post your attempt and any rough work that pertains to this problem.

I've graphed it, but that still doesn't get me any where I don't know which integral to set it up with.

Ok this is what i got probably wrong. V=$$\pi$$ (integral) [x2-1] dy

with the lower limit of the integral being 0 and the top being 2

What does the region that will be revolved around the y-axis look like? Have you drawn a sketch of the revolved solid. Are you going to use shells or disks to get the volume?

What expression represents your typical volume element?

## 1. What is an integral and why is it important?

An integral is a mathematical concept that represents the accumulation or total value of a quantity over a given interval. It is important because it allows us to calculate the area under a curve, which has many real-life applications such as finding the total distance traveled by an object or the total amount of water in a reservoir.

## 2. How do I set up an integral?

To set up an integral, you first need to determine the function that represents the quantity you want to find the total value of. Then, you need to identify the limits of integration, which are the starting and ending points of the interval. Finally, you need to decide whether you will use the definite or indefinite form of the integral and set up the appropriate notation.

## 3. What are the different types of integrals?

There are two types of integrals: definite and indefinite. A definite integral has specific limits of integration and gives a single numerical value as the result. An indefinite integral does not have limits of integration and gives a function as the result, which can be evaluated at different points.

## 4. How do I know which method to use for solving an integral?

There are several methods for solving integrals, such as integration by substitution, integration by parts, and using trigonometric identities. The best method to use depends on the complexity of the function and the limits of integration. It is helpful to practice using different methods to become more familiar with them.

## 5. Can you provide an example of setting up an integral?

Sure, let's say we want to find the area under the curve of the function f(x) = x^2 from x = 0 to x = 2. We can set up the definite integral as ∫(0 to 2) x^2 dx. This notation represents the accumulation of the function x^2 from 0 to 2, which will give us the area under the curve. From here, we can solve the integral using the appropriate method and find the numerical value of the area.

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