Lecture 6 Change of variables in multiple integrals

Lecture 6 Change of variables in multiple integrals In this lecture we study • Change of variables in double integrals • Change of variables in triple integrals • Surface area

Lecture 6 Change of variables in multiple integrals Sometime, we are asked to integrate over a two (or three) dimensional region that would have been somewhat difficult to integrate over it. Therefore, we have to change variables in the integral, this change of variables converts the region into a region that would be much easier in integrate over. In addition to converting the integrand into something simpler to deal with we often also transform the region into another.

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals Now we give the rule for change of variables in a double integral.

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals Under the given transformation we get

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in double integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Change of variables in triple integrals

Lecture 6 Surface Area

Lecture 6 Surface Area