BE Biotechnology छमाही २ (इंजीनियरिंग) - University of Mumbai Important Questions for Applied Mathematics 2

Use polar co ordinates to evaluate `int int (x^2+y^2)^2/(x^2y^2)` 𝒅𝒙 𝒅𝒚 over yhe area Common to circle `x^2+y^2=ax  "and" x^2+y^2=by, a>b>0`

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.

Evaluate `int int intx^2dxdydz` over the volume bounded by planes x=0,y=0, z=0 and `x/a+y/b+z/c=1`

Change the order of integration and evaluate `int_0^2 int_(2-sqrt(4-y^2))^(2+sqrt(4-y^2)) dxdy` 

Find by double integration the area bounded by the parabola 𝒚𝟐=𝟒𝒙 And 𝒚=𝟐𝒙−𝟒 

Find the volume bounded by the paraboloid 𝒙^𝟐+𝒚^𝟐=𝒂𝒛 and the cylinder 𝒙^𝟐+𝒚^𝟐=𝒂^𝟐. 

Change to polar coordinates and evaluate `int_0^1 int_0^x (x+y)dydx`