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2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi- tuting x = u + 2v and y = u – v, calculate

2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi- tuting x = u + 2v and y = u – v, calculate

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 39E
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Vector Calculus. Please write clearly and each computation step for the question. Need steps，thanks q2
1. By switching to polar coordinates, calculate 4-x2 x² dy dx. 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi- tuting x = u + 2v and y = u – v, calculate (x + 2y)²e²-y. D 3. Let R be the solid cone in R³ whose base is the standard unit circle (given by x² + y² z = 0) and whose vertex is the point (0, 0, 1). Calculate = 1 and 22 dV.
Transcribed Image Text:1. By switching to polar coordinates, calculate 4-x2 x² dy dx. 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi- tuting x = u + 2v and y = u – v, calculate (x + 2y)²e²-y. D 3. Let R be the solid cone in R³ whose base is the standard unit circle (given by x² + y² z = 0) and whose vertex is the point (0, 0, 1). Calculate = 1 and 22 dV.
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