How do you find the volume bounded by #y = 2x^(1/2)#, the line y = 2 and x = 4 revolved about y=2?

Answer 1

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Answer 2

To find the volume bounded by ( y = 2x^{1/2} ), the line ( y = 2 ), and ( x = 4 ) revolved about ( y = 2 ), you can use the method of cylindrical shells.

The volume ( V ) can be calculated using the formula:

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

where ( a ) and ( b ) are the limits of integration, and ( f(x) ) and ( g(x) ) are the functions defining the boundaries.

In this case, ( f(x) = 2x^{1/2} ), ( g(x) = 2 ), and ( a = 0 ), ( b = 4 ). So, plug these values into the formula and evaluate the integral to find the volume.

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Answer from HIX Tutor

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.