# How to answer these using intergration ?

The area is

Start by finding the intercept with the x-axis

Therefore,

The area is

The volume is

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a.

b.

Now we know our upper and lower bounds.

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To answer questions using integration, you need to follow these steps:

- Understand the problem and identify what needs to be integrated.
- Set up the integral using appropriate notation.
- Evaluate the integral using integration techniques such as substitution, integration by parts, trigonometric substitutions, or partial fractions.
- Check your solution by differentiating the result and ensuring it matches the original function, if applicable.
- Simplify the answer as much as possible, and include any necessary constants of integration.

If you have specific questions or examples, feel free to ask for further clarification or guidance.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you use an integral to find the volume of a solid torus?
- How do you find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 5?
- The region under the curves #x=0, x=y-y^4# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
- Find the area of the region bounded by the curves?
- How do you find the area between #y=x^2# and #y=8x#?

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