The volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.
What is integration?
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
y = 3 - x
From the graph:
Shell radius = y
Height = 3 - y
From the shell method, we can write the integral as follows:
[tex]\rm Volume =2\pi\int\limits^0_{-3} {y(3-y)} \, dy[/tex]
[tex]\rm Volume =2\pi\int\limits^0_{-3} {(3y-y^2)} \, dy[/tex]
After solving the above definite integral, we will get volume:
Volume = 9π cubic units
Thus, the volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.
Learn more about integration here:
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