Can someone help me please?? in Algblra2 - Variations, Progression, and Theorems
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If and
have the same sign, then either
or
If and
have opposite sign, then
or
This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set
The area of is given by the double integral
To compute the area, change the variables to
The Jacobian for this transformation is
with determinant . Then the integral transforms to
which is 1/12 the area of a square with side length 12. Hence the integral evaluates to
.