16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
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GROUP WORK 1, SECTION <strong>16</strong>.9<br />
Many Changes of Variables<br />
1. We wish to find ∫∫ R xy2 dA,whereR is given below.<br />
Hint: Use a change of variables to create an equivalent integral over a rectangular region in the uv-plane.<br />
2. Find a mapping T which maps the triangle bounded by (0, 0), (0, 1), and(1, 0) to the triangle bounded<br />
by (0, 0), (5, 2),and(5, −2). What is the Jacobian of T ? What is the area of R?<br />
930
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