# The region under the curves #y=xe^(x^3), 1<=x<=2# is rotated about the x axis. How do you find the volumes of the two solids of revolution?

There is only on solid of revolution generated by this description.

Use a calculator if you want a decimal approximation.

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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 fast is the volume changing with respect to time when the radius is changing with respect to time when the radius is changing at a rate of dr/dt=1.5 feet per second and r=2 feet?
- The region under the curves #y=x^2, y=x# 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?
- How do you find the volume of a solid that is enclosed by #y=3x^2# and y=2x+1 revolved about the x axis?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs of the equations #y=sec(x)# , y=0, #0 <= x <= pi/3# about the line y = 5?
- How do you find #\int _ { 4} ^ { 9} \frac { x + 1} { x+ 2\sqrt { x } - 3} d x#?

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