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Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two curves start and end at the same points. a. Ci is the curve y = 2x² with x ranging from -1 to +1. Draw a graph showing the curve Ci and then calculate (F-dr. b. Cz is the straight line that goes from x =-1, y= 2 to x = 1, y = 2. Draw a graph showing the curve C2 and then calculate [F•dr. As a check in this question you should get the same answer for both integrals because the vector field F = 3x°yi + xj is the gradient of an associated scalar function , f (x, y) =x³yand C1 and C2 start and end at the same points.

Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two curves start and end at the same points. a. Ci is the curve y = 2x² with x ranging from -1 to +1. Draw a graph showing the curve Ci and then calculate (F-dr. b. Cz is the straight line that goes from x =-1, y= 2 to x = 1, y = 2. Draw a graph showing the curve C2 and then calculate [F•dr. As a check in this question you should get the same answer for both integrals because the vector field F = 3x°yi + xj is the gradient of an associated scalar function , f (x, y) =x³yand C1 and C2 start and end at the same points.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Calculate the line integral (F•dr, where F 3x yi + x'j in two cases for Ci and C2. These two curves start and end at the same points. a. Ci is the curve y = 2x² with x ranging from -1 to +1. Draw a graph showing the curve Ci and then calculate (F•dr. b. Cz is the straight line that goes from x = -1, y = 2 to x = 1, y = 2. Draw a graph showing the curve C2 and then calculate [F•dr. As a check in this question you should get the same answer for both integrals because the vector field F = 3x° yi + x'j is the gradient of an associated scalar function , f (x, y) = x³y and C1 and C2 start and end at the same points.
Transcribed Image Text:Calculate the line integral (F•dr, where F 3x yi + x'j in two cases for Ci and C2. These two curves start and end at the same points. a. Ci is the curve y = 2x² with x ranging from -1 to +1. Draw a graph showing the curve Ci and then calculate (F•dr. b. Cz is the straight line that goes from x = -1, y = 2 to x = 1, y = 2. Draw a graph showing the curve C2 and then calculate [F•dr. As a check in this question you should get the same answer for both integrals because the vector field F = 3x° yi + x'j is the gradient of an associated scalar function , f (x, y) = x³y and C1 and C2 start and end at the same points.
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