# Assignments

Integration can be used for the calculation of an area. This means that the corresponding function has to be integrated, taking into account the limits of integration: the so-called lower and upper boundaries.
When integration is used to calculate the content of solids of revolution there are two formulas of interest: one for the rotation of a graph around the -axis, the other around the -axis. Sometimes we need to do some preparations before the integral can be calculated.

1. Calculate the area which is enclosed by the graph of , the -axis and the line .

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2. Calculate the are which is enclosed by , the lines , and .

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3. Calculate the area which is enclosed by the lines and and the graph of the quadratic function . This assignment is relevant for the calculation of the Producer Surplus (see Bradley T. en Patton P., Essential Mathematics for Economics and Business, 2e ed., John Wiley, p. 418).

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4. Calculate the area which is enclosed by the lines and and the graph of the function .
This assignment is relevant for the calculation of the Producer Surplus (see Bradley T. en Patton P., Essential Mathematics for Economics and Business, 2e ed., John Wiley, p. 416).

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5. Calculate the area which is enclosed by the circle , that is a circle with center and radius .

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6. Calculate the volume of the cylinder which is the result of revolving the line , around the -axis.

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7. Calculate the content of the cone which is the result of revolving the line , around the -axis.

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8. Calculate the volume of the sphere with center and radius .

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9. Calculate the volume of the paraboloid which is the result of revolving the parabola , around the -axis.

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10. Suppose we have a sphere with radius . We drill a cylinder in this sphere. The axis of the cylinder goes through the center of the sphere (compare a corer). After the drill it appears that the cylinder has a height of with . Calculate the volume of the spherical shell that remains after the cylinder has been drilled.

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