Revision: Triple Integration and Applications of Multiple Integrals Applied Mathematics 2 BE Civil Engineering Semester 2 (FE First Year) University of Mumbai
- Evaluate ∫ ∫ ∫ √ 1 − X 2 a 2 − Y 2 B 2 − X 2 C 2 Dx Dy Dz Over the Ellipsoid X 2 a 2 + Y 2 B 2 + Z 2 C 2 = 1 .
- Find the Volume Enclosed by the Cylinder Y 2 = X and Y = X 2 Cut off by the Planes Z = 0, X+Y+Z=2.
- Find the Volume of the Paraboloid X 2 + Y 2 = 4 Z Cut off by the Plane 𝒛=𝟒
- Use Polar Co Ordinates to Evaluate ∫ ∫ ( X 2 + Y 2 ) 2 X 2 Y 2 𝒅𝒙 𝒅𝒚 Over Yhe Area Common to Circle X 2 + Y 2 = a X and X 2 + Y 2 = B Y , a > B > 0
- Find the Area Inside the Circle R=A Sin𝜽 and Outside the Cardioide R=A(1+Cos𝜽 )
- Evaluate ∫ ∫ X Y ( X − 1 ) D X D Y Over the Region Bounded by 𝒙𝒚 = 𝟒,𝒚= 𝟎,𝒙 =𝟏 and 𝒙 = 𝟒
- Evaluate ∫ ∫ 2 X Y 5 √ X 2 Y 2 − Y 4 + 1 D X D Y , Where R is Triangle Whose Vertices Are (0,0),(1,1),(0,1).
- Find by Double Integration the Area Bounded by the Parabola 𝒚𝟐=𝟒𝒙 and 𝒚=𝟐𝒙−𝟒
- Change to Polar Coordinates and Evaluate ∫ 1 0 ∫ X 0 ( X + Y ) D Y D X
- Find the Volume Bounded by the Paraboloid 𝒙𝟐+𝒚𝟐=𝒂𝒛 and the Cylinder 𝒙𝟐+𝒚𝟐=𝒂𝟐.
- Find the Mass of a Lamina in the Form of an Ellipse X 2 a 2 + Y 2 B 2 = 1 , If the Density at Any Point Varies as the Product of the Distance from the The Axes of the Ellipse.
- Change the Order of Integration and Evaluate ∫ 2 0 ∫ 2 + √ 4 − Y 2 2 − √ 4 − Y 2 D X D Y
- Evaluate ∫ ∫ ∫ X 2 D X D Y D Z Over the Volume Bounded by Planes X=0,Y=0, Z=0 and X a + Y B + Z C = 1
