Need help with part g. 1. In this workshop, we are going to explore formulas for areas and arc length associated to curves writtenin polar coordinates. We'll do this by using the formulas to compute areas and lengths of well-knownobjects (and, in most cases, checking our answers).Here is the formula for the area bounded by r = f(0) and the rays 0 = a and 0 = ß:A :(S(C(a) Consider the circle of radius 2 centered at the origin. Write down an integral in polar coordinatesthat gives the area inside the circle. Evaluate your integral, and check that you get the correctanswer. What would change if you only wanted to find the area of the quarter-circle in the secondquadrant?(b) Now, let's make our circle of radius 2 not centered at the origin, but instead at (2, 0). What isr = f(0) in this case? (If you were paying attention, we did this in our last class.) Write down anintegral in polar coordinates that gives the area inside the circle. (Be careful with your bounds.)Evaluate your integral, and check that you get the correct answer.How about other shapes?(c) Consider the triangle with vertices at (0,0), (5,0), and (5,5). Write down an integral in polarcoordinates that gives the area of this triangle. (You can do this with exactly one integral.) Evaluateyour integral, and check that you get the correct answer (you should know what the correct answeris).(d) Consider the rectangular region defined by 1 < r < 3 and 0 < y < 2. Write down one or moreintegrals in polar coordinates to find the area of the region. (You may need to add or subtract twoor more integrals to achieve this.) You do not need to evaluate these integrals.We also have a formula for the arc length of a curve r = {(0) defined in polar coordinates:s = /' vt@)² + (s"(0)² d0 (e) Write down an integral for the circumference of the circle of radius 2 centered at the origin. Evaluateyour integral, and check that you get the correct answer.(f) Now, let's make our circle of radius 2 not centered at the origin, but instead at (2,0). Write downan integral in polar coordinates that gives the circumference of the circle. (Be careful with yourbounds.) Evaluate your integral, and check that you get the correct answer.(g) Consider the line segment from (1, 1) to (0, 1). Write down an integral that computes the length ofthis line segment, using polar coordinates. Evaluate your integral, and check that you obtain thecorrect answer. (You'll need to use some trigonometric identities here.)

Name: Need help with part g. 1. In this workshop, we are going to explore fo
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Description: Need help with part g. 1. In this workshop, we are going to explore formulas for areas and arc length associated to curves writtenin polar coordinates. We'll do this by using the formulas to compute areas and lengths of well-knownobjects (and, in mos

The line segments joining the points (1,1) to (0,1) will be part of the horizontal line y=1. Thus…

Math

Calculus

(g) Consider the line segment from (1, 1) to (0, 1). Write down an integral that computes the length of this line segment, using polar coordinates. Evaluate your integral, and check that you obtain the correct answer. (You'll need to use some trigonometric identities here.)

(g) Consider the line segment from (1, 1) to (0, 1). Write down an integral that computes the length of this line segment, using polar coordinates. Evaluate your integral, and check that you obtain the correct answer. (You'll need to use some trigonometric identities here.)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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