Triple Integral of z over [0, 2*pi] for r [1, 2]

In summary, a triple integral is a mathematical tool used to calculate the volume under a three-dimensional surface. It involves finding the area under the surface at each point in the x-y plane and then integrating those areas along the z-axis. The notation "z over [0, 2*pi]" in a triple integral indicates that the function being integrated is dependent on both x and y, and the integration is being done over the entire range of z values. Similarly, "r [1, 2]" signifies that the function being integrated is dependent on both x and y, and the integration is being done over the range of r values between 1 and 2. The limits of integration in a triple integral define the boundaries within which the integration
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kasse
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[SOLVED] Triple integral

Homework Statement



Calculate the triple integral of z when z [(r-1), sqrt(1-(r-2)^2)], r [1, 2], tetha [0, 2*pi]

2. The attempt at a solution

I've tried again and again, and I always get (17/4)*pi, while the answer is pi/2. Is there anything wrong with antiderivating in this order: dz, dr, d(tetha)?
 
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Related to Triple Integral of z over [0, 2*pi] for r [1, 2]

What is a triple integral?

A triple integral is an integral that calculates the volume under a three-dimensional surface. It is calculated by finding the area under the surface at each point in the x-y plane and then integrating those areas along the z-axis.

What is the meaning of "z over [0, 2*pi]" in the triple integral?

This notation means that the variable z is being integrated from 0 to 2*pi, which is the range of values for the z-axis. This indicates that the function being integrated is dependent on both x and y, and the integration is being done over the entire range of z values.

What does "r [1, 2]" signify in the triple integral?

The notation "r [1, 2]" indicates that the variable r is being integrated from 1 to 2. This means that the function being integrated is dependent on both x and y, and the integration is being done over the range of r values between 1 and 2.

What is the significance of the limits of integration in a triple integral?

The limits of integration in a triple integral define the boundaries within which the integration is being performed. These limits determine the range of values for each variable (x, y, and z) and the volume over which the function is being integrated.

How is a triple integral calculated?

A triple integral is calculated by first finding the areas under the surface at each point in the x-y plane. These areas are then integrated along the z-axis, and the resulting values are integrated again along the x and y axes to find the total volume under the surface.

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