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3.1 Using the differential length dl, find the length of each of the following curves: (a) p = 3, T/4 < ¢ < «/2, z = constant (b) r = 1, 0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° < 0 < 90°, 6 = constant

3.1 Using the differential length dl, find the length of each of the following curves: (a) p = 3, T/4 < ¢ < «/2, z = constant (b) r = 1, 0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° < 0 < 90°, 6 = constant

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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3.1 Using the differential length dl, find the length of each of the following curves: (a) p = 3, T/4 < ¢ < «/2, z = constant (b) r = 1, 0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° < 0 < 90°, ¢ = constant 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2, 0 < z < 5, 7/3 < ¢ < T/2 (b) z = 1, 1 < p < 3,0 < ¢ < T/4 (c) r = 10, 7/4 < 0 < 2#/3, 0 < ¢ < 2™ (d) 0 < r < 4, 60° < 0 < 90°, ø = constant
Transcribed Image Text:3.1 Using the differential length dl, find the length of each of the following curves: (a) p = 3, T/4 < ¢ < «/2, z = constant (b) r = 1, 0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° < 0 < 90°, ¢ = constant 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2, 0 < z < 5, 7/3 < ¢ < T/2 (b) z = 1, 1 < p < 3,0 < ¢ < T/4 (c) r = 10, 7/4 < 0 < 2#/3, 0 < ¢ < 2™ (d) 0 < r < 4, 60° < 0 < 90°, ø = constant
2.10 Express the following vectors in rectangular coordinates: (а) А psin ф a, + р cos ф а, 2z az - (b) В — 4r cos ф а, + rao
Transcribed Image Text:2.10 Express the following vectors in rectangular coordinates: (а) А psin ф a, + р cos ф а, 2z az - (b) В — 4r cos ф а, + rao
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