# How do you find the volume bounded by x = 1, x = 2, y = 0, and #y = x^2 # revolved about the x-axis?

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To find the volume bounded by ( x = 1 ), ( x = 2 ), ( y = 0 ), and ( y = x^2 ) revolved about the x-axis, you would use the method of cylindrical shells.

The formula to find the volume using cylindrical shells is:

[ V = 2\pi \int_{a}^{b} x \cdot f(x) , dx ]

Where ( f(x) ) represents the height of the shell at the given ( x )-value.

In this case, ( a = 1 ), ( b = 2 ), and ( f(x) = x^2 ).

So, the integral to find the volume becomes:

[ V = 2\pi \int_{1}^{2} x \cdot (x^2) , dx ]

Solve this integral to find the volume.

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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.

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