A parallelogram in the plane is bounded by the four lines ,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Vector calculus and field geometry

Mathematical Methods for Physics, Ch Multiple integrals and change of variables

Problem

A parallelogram

P

in the

xy

plane is bounded by the four lines

x+y=0

x+y=1

x-2y=0

and

x-2y=3

. ((a)) Using the new coordinates

u=x+y

v=x-2y

, describe

P

in the

(u,v)

plane and find

|J|

. ((b)) Find the area of

P

and the value of

\iint_P (x+y)^2\,\mathrm{d}A

. ((c)) What area would you get if you left out

|J|

? Explain why checking units would not catch that slip here.

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