16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
GROUP WORK 2, SECTION <strong>16</strong>.9<br />
Transformed Parabolas<br />
Consider the change of variables x = u 2 − v 2 , y = 2uv described in Example 1 of the text.<br />
1. Compute ∫∫ R x2 dA,whereR is the region shown below.<br />
Hint: How is ∫∫ R x2 dArelated to ∫∫ R 1<br />
x 2 dA,whereR 1 is the portion of R above the x-axis?<br />
2. Let S be the rectangle {(u,v) | 0 ≤ u ≤ 1, 0 ≤ v ≤ 2}. What is the image T in the xy-plane of S under<br />
this change of variables?<br />
3. What is the area of T ?<br />
931
Change language