√無料でダウンロード！ paraboloide z=x^2 y^2 204313

find the volume of solid inside the paraboloid z=9x^2y^2, outside the cylinder x^2y^2=4 and above the xyplane 1) solve using double integration of rectangular coordinate 2) solve using double integration of polar coordinate Math A solid body consists of a cylinder surmounted by a hemisphere of the same radius

Paraboloide z=x^2 y^2-Unformatted text preview !yxx!Solving z = y and either paraboloid equation simultaneously gives us that the projection of the volume onto the xy plane is the area whose equation is y = x^2 y^2 which can be rearranged as x^2 (y 1/2)^2 = (1/2)^2 which is a circle of radius 1/2 centred on (0, 1/2) So the required volume = 2 integral (that circle) y (x^2 y^2) dy dx