Labware - MA35 Multivariable Calculus - Two Variable Calculus
 MA35 Labs 2 » Two Variable Calculus Contents2.4 Integration 2.4.2 Riemann Integral 2.4.4 Change of Order of Integration 2.4.6 Change of Variables 2.4.8 Center of Mass 2.4.9 Moment of Inertia Search

Change of Order of Integration (Page: 1 | 2 )

Text

If we apply Fubini's Theorem to integrals using polar coordinates, we get

abcdf(x, y)rdrdθ = ∫cdabf(x, y)rdθdr = ∫∫Rf(r, θ)dA

Where dA = dr*dθ.

Demos

 Change of Order of Integration In this demo, start with "step" and "step2" set to their minimum values. Increase "step" to its maximum first and then increase "step2" to its maximum to represent integration with respect to r first and θ second. To see the alternative order of integration, increase "step2" first.

Exercises

• One of the change of order of integration demos for Cartesian coordinates discusses "slab approximations". What would slabs look like in polar coordinates? How would you use summation and integral notation to describe slab approximations in polar coordinates?