3 Let R be the region inside the curve C :r = 1+cos 0 and to the right of the line € : r = - sec 0. 2.1. Find the polar points of intersection of C and € whose 0-coordinate are in [-a, a]. Hint: Let u = cos 0. And then later in your computation, recall that for all 0 e R, –1 < cos 0 < 1. 2.2. Sketch C and € in one polar coordinate system. Indicate their polar points of intersection. 2.3. Set-up and evaluate the integrals that gives the perimeter of R. Hint: For the length of C, after you simplify the radicand, rationalise your integrand. Remember that 1- cos? 0 = sin² 0. And then finally, use integration by substitution. %3D
3 Let R be the region inside the curve C :r = 1+cos 0 and to the right of the line € : r = - sec 0. 2.1. Find the polar points of intersection of C and € whose 0-coordinate are in [-a, a]. Hint: Let u = cos 0. And then later in your computation, recall that for all 0 e R, –1 < cos 0 < 1. 2.2. Sketch C and € in one polar coordinate system. Indicate their polar points of intersection. 2.3. Set-up and evaluate the integrals that gives the perimeter of R. Hint: For the length of C, after you simplify the radicand, rationalise your integrand. Remember that 1- cos? 0 = sin² 0. And then finally, use integration by substitution. %3D
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
Let R be the region inside the curve C :r=1+cos 0 and to the right of the line € : r = sec 0.
2.1. Find the polar points of intersection of C and { whose 0-coordinate are in [-a, 7].
Hint: Let u = cos 0. And then later in your computation, recall that for all 0 E R, –1< cos 0 < 1.
2.2. Sketch C and € in one polar coordinate system. Indicate their polar points of intersection.
2.3. Set-up and evaluate the integrals that gives the perimeter of R.
Hint: For the length of C, after you simplify the radicand, rationalise your integrand. Remember that
1- cos? 0 = sin² 0. And then finally, use integration by substitution.
2.4. Set up but do not evaluate the integral that gives the area of R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81d8123d-7e02-48d0-b30d-f764a031f5a0%2F15301891-ab5d-4209-b2c0-d1c1eee25e40%2Ft4f5n6b_processed.png&w=3840&q=75)
Transcribed Image Text:3
Let R be the region inside the curve C :r=1+cos 0 and to the right of the line € : r = sec 0.
2.1. Find the polar points of intersection of C and { whose 0-coordinate are in [-a, 7].
Hint: Let u = cos 0. And then later in your computation, recall that for all 0 E R, –1< cos 0 < 1.
2.2. Sketch C and € in one polar coordinate system. Indicate their polar points of intersection.
2.3. Set-up and evaluate the integrals that gives the perimeter of R.
Hint: For the length of C, after you simplify the radicand, rationalise your integrand. Remember that
1- cos? 0 = sin² 0. And then finally, use integration by substitution.
2.4. Set up but do not evaluate the integral that gives the area of R.
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