Question

Using change of variables principle in double integral we can reduce cartesian integral to simpler form.

(a) True

(b) False

The question was asked during an online exam.

My question is based upon Change of Variables In a Double Integral in chapter Multiple Integrals of Engineering Mathematics

Answer 1

Correct choice is (a) True

To elaborate: The above statement is not necessarily true always but change of variables cartesian to polar form & changing into suitable form reduces the complexity in the evaluation of double integral however converse is also true  for example ∬R x^2 y^3 dx dy is the given integral while solving there is no need of converting it into polar form since ∬P r^6 cos^2 θ sin^3 θ dr dθ is tedious to solve when R  only consists of  constants but  ∬R x^2 y^3 dx dy can be solved easily by ordinary method of integration.