differential equation
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1) A lamina has the shape region in the xy-plane bounded by the graphs of
y = (25-x^2)^(1/2) , y = 0, x = 3, x = 5
If the density (in kg/m^3) at each point P in is inversely proportional to the square of the distance from P to the y-axis, with (5,0,0) = 1 kg/m^3. Find the mass of the lamina [Assume a constant thickness of 0.01 m]
2) Consider region in the xy-plane bounded by the graphs of
y = sec(x) tan(x), y = 0, x= 0, x = /4
If the region is revolved about the y - axis we obtain the solid of revolution Q. Find the volume of Q. [distance in meters]
3) Consider region in the xy-plane bounded by the graphs of
y = sec(x) tan(x), y = 0, x = 0, x = /4
If the region is revolved about the x-axis we obtain the solid of revolution Q. Find the volume of Q [distance in meters]
4) Solve the differential equation: dy/dx = 1/3xe^(x^(1/3)) with y(0) =1
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Solution Summary
The differential equation is assessed for the total mass of the lamina.
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