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RK7
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Homework Statement
Find the volume of the enclosed by the surfaces [tex]z=qx[/tex] [tex]z=0[/tex] and [tex]x²+y²=2ax[/tex]
Homework Equations
This is meant to be done with calculus but can verify my answer with simple geometry - should be [tex]\pi a^3q[/tex]
The Attempt at a Solution
So the top of the wedge will be when [tex]x=2a[/tex]
Form rectangular slices of the wedge perpendicular to the x-axis with area [tex]A=2yz=2\sqrt{x(2a-x)}qx[/tex] and volume [tex]2\sqrt{x(2a-x)}qx .dx[/tex]
Then integrate this from x=0 to x=2a gives:
V=[itex]\int ^{2a} _{0} 2q \sqrt{x^{3}(2a-x)} dx[/itex]
I've checked this numerically with wolfram alpha for certain values of a and q but I haven't got a clue how to evaluate it.. the question said to use a double integral but I don't know what a suitable double integral would be...