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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 15.3 : Double Integrals over General Regions
- Evaluate ∬D8yx3dA where D={(x,y)|−1≤y≤2,−1≤x≤1+y2}
- Evaluate ∬D12x2y−y2dA where D={(x,y)|−2≤x≤2,−x2≤y≤x2}
- Evaluate ∬D9−6y2x2dA where D is the region in the 1st quadrant bounded by y=x3 and y=4x.
- Evaluate ∬D15x2−6ydA where D is the region bounded by x=12y2 and x=4√y.
- Evaluate ∬D6y(x+6)2dA where D is the region bounded by x=−y2 and x=y−6.
- Evaluate ∬Dey2+1dA where D is the triangle with vertices (0,0), (−2,4) and (8,4).
- Evaluate ∬D7y3ex2+1dA where D is the region bounded byy=24√x, x=9 and the x-axis.
- Evaluate ∬Dx5sin(y4)dA where D is the region in the 2nd quadrant bounded by y=3x2, y=12 and the y-axis.
- Evaluate ∬Dxy−y2dA where D is the region shown below.
- Evaluate ∬D12x3−3dA where D is the region shown below.
- Evaluate ∬D6y2+10yx4dA where D is the region shown below.
- Evaluate ∬Dx3y2dA where D is the region bounded by y=1x2, x=1 and y=14 in the order given below.
- Integrate with respect to x first and then y.
- Integrate with respect to y first and then x.
- Evaluate ∬Dxy−y3dA where D is the region bounded by y=x2, y=−x2 and x=2 in the order given below.
- Integrate with respect to x first and then y.
- Integrate with respect to y first and then x.
For problems 14 – 16 evaluate the given integral by first reversing the order of integration.
- ∫80∫2y13yx7+1dxdy
- ∫0−4∫2√−xx−23√y53+1dydx
- ∫20∫3x−x5y2x3+2dydx
- Use a double integral to determine the area of the region bounded by x=−y2 and x=y−6.
- Use a double integral to determine the area of the region bounded by y=x2+1 and y=12x2+3.
- Use a double integral to determine the volume of the region that is between the xy‑plane and f(x,y)=2−xy2 and is above the region in the xy-plane that is bounded by y=x2 and x=1.
- Use a double integral to determine the volume of the region that is between the xy‑plane and f(x,y)=1+y5√x4+1 and is above the region in the xy-plane that is bounded by y=√x, x=2 and the x-axis.
- Use a double integral to determine the volume of the region in the first octant that is below the plane given by 2x+6y+4z=8.
- Use a double integral to determine the volume of the region bounded by z=3−2y, the surface y=1−x2 and the planes y=0 and z=0.
- Use a double integral to determine the volume of the region bounded by the planes z=4−2x−2y, y=2x, y=0 and z=0.
- Use a double integral to determine the formula for the area of a right triangle with base, b and height h.
- Use a double integral to determine a formula for the figure below.