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Calculus 3: Double integrals

Using double integrals, find the volume under a given multivariable function.

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Compute the volume under the surface given by f(x,y)=9x2y2f(x, y) = 9 - x^2 - y^2 over the rectangular region where xx is between 2-2 and 22 and yy is between 2-2 and 22.

Set up a generic integral for the region bounded by the curves y=4xy = 4x and y=x3y = x^3, using the order of iteration dy/dxdy/dx.

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Compute the volume under the surface given by f(x,y)=9x2y2f(x, y) = 9 - x^2 - y^2 over the rectangular region where xx is between 2-2 and 22 and yy is between 2-2 and 22.

Set up a generic integral for the region bounded by the curves y=4xy = 4x and y=x3y = x^3, using the order of iteration dy/dxdy/dx.

Given an iterated integral with a function having y5+1y^5 + 1 in the denominator, reverse the order of integration to simplify the integral.

Find the volume of the solid bounded by the surfaces z=y+1z = y + 1 and z=x2+1z = x^2 + 1 over the region where y=x2y = x^2 and y=1y = 1.

Find the area bounded by the curves y=x2y = x^2 and x=4x = 4 using the double integral technique.

Solve a double integral problem using the Fundamental Theorem of Calculus.

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Compute the volume under the surface given by f(x,y)=9x2y2f(x, y) = 9 - x^2 - y^2 over the rectangular region where xx is between 2-2 and 22 and yy is between 2-2 and 22.

Set up a generic integral for the region bounded by the curves y=4xy = 4x and y=x3y = x^3, using the order of iteration dy/dxdy/dx.

Given an iterated integral with a function having y5+1y^5 + 1 in the denominator, reverse the order of integration to simplify the integral.

Find the volume of the solid bounded by the surfaces z=y+1z = y + 1 and z=x2+1z = x^2 + 1 over the region where y=x2y = x^2 and y=1y = 1.

Find the area bounded by the curves y=x2y = x^2 and x=4x = 4 using the double integral technique.

Solve a double integral problem using the Fundamental Theorem of Calculus.

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Compute the volume under the surface given by f(x,y)=9x2y2f(x, y) = 9 - x^2 - y^2 over the rectangular region where xx is between 2-2 and 22 and yy is between 2-2 and 22.