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1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = 0 and a? + y? = 4. Note that these curves divide the plane into 3 separate regions, which have been marked on the diagram.

1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = 0 and a? + y? = 4. Note that these curves divide the plane into 3 separate regions, which have been marked on the diagram.

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 61E
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(0,2) 1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = ( and x? + y? = 4. Note that these curves divide the plane into 3 separate regions, which have been marked on the diagram. R1 (0,1) R2 (0,0) R3 (a) Write fR. 2x dA as an iterated integral, both in the "dx dy" order and in the "dy dx" order. Then, evaluate one of the two integrals. (0,-2). (b) Set up fr 2x dA as an iterated integral, both in the "dx dy" order and in the "dy dx" order. (c) Use polar coordinates to evaluate fa (x² + y?) dA. (d) Use polar coordinates to evaluate fp 12x dA, where R is the region formed by combining the regions R1 and R2. (e) Set up, but do not evaluate, an iterated integral equivalent to fs 2x dA, where S is the region formed by combining the regions R2 ad R3. Use whatever coordinate system you think is easiest.
Transcribed Image Text:(0,2) 1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = ( and x? + y? = 4. Note that these curves divide the plane into 3 separate regions, which have been marked on the diagram. R1 (0,1) R2 (0,0) R3 (a) Write fR. 2x dA as an iterated integral, both in the "dx dy" order and in the "dy dx" order. Then, evaluate one of the two integrals. (0,-2). (b) Set up fr 2x dA as an iterated integral, both in the "dx dy" order and in the "dy dx" order. (c) Use polar coordinates to evaluate fa (x² + y?) dA. (d) Use polar coordinates to evaluate fp 12x dA, where R is the region formed by combining the regions R1 and R2. (e) Set up, but do not evaluate, an iterated integral equivalent to fs 2x dA, where S is the region formed by combining the regions R2 ad R3. Use whatever coordinate system you think is easiest.
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