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Problem 3. Consider the integral Using the area interpretation of the definite integral, convince yourself that the expression represents the area of a circle of radius R. (We have seen very similar examples in class and in Homework 1 and your first TUC contained such an integral.) We want to study the particular case when R = 3, i.e., (c) 4 √ √9 - x² dx. (1) to illustrate a special kind of substitution. Let x = 3 sin 0 and assume is between -π/2 and π/2. integral as (d) R 4 [²³ 36 R²-x² dx. Using the trigonometric identity cos² 0 = (1 + cos(20)), we can rewrite the new *π/2 Evaluate this definite integral. co cos²0 de = 18 Cπ/2 (1 + cos(20)) de. Did you find that the definite integral is 32π = 9, as expected?

Problem 3. Consider the integral Using the area interpretation of the definite integral, convince yourself that the expression represents the area of a circle of radius R. (We have seen very similar examples in class and in Homework 1 and your first TUC contained such an integral.) We want to study the particular case when R = 3, i.e., (c) 4 √ √9 - x² dx. (1) to illustrate a special kind of substitution. Let x = 3 sin 0 and assume is between -π/2 and π/2. integral as (d) R 4 [²³ 36 R²-x² dx. Using the trigonometric identity cos² 0 = (1 + cos(20)), we can rewrite the new *π/2 Evaluate this definite integral. co cos²0 de = 18 Cπ/2 (1 + cos(20)) de. Did you find that the definite integral is 32π = 9, as expected?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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Problem 3. Consider the integral Using the area interpretation of the definite integral, convince yourself that the expression represents the area of a circle of radius R. (We have seen very similar examples in class and in Homework 1 and your first TUC contained such an integral.) We want to study the particular case when R = 3, i.e., 3 4.6.³. (1) 0 to illustrate a special kind of substitution. Let x = 3 sin and assume is between -π/2 and π/2. R 4 /³² 36 (d) R² - x² dx. (c) Using the trigonometric identity cos² 0 = (1 + cos(20)), we can rewrite the new integral as π/2 Evaluate this definite integral. √9 - x² dx. cos2 Ꮎ d0 = 18 3 ™1² 0 (1 + cos(20)) do. Did you find that the definite integral is 3²π = 9π, as expected?
Transcribed Image Text:Problem 3. Consider the integral Using the area interpretation of the definite integral, convince yourself that the expression represents the area of a circle of radius R. (We have seen very similar examples in class and in Homework 1 and your first TUC contained such an integral.) We want to study the particular case when R = 3, i.e., 3 4.6.³. (1) 0 to illustrate a special kind of substitution. Let x = 3 sin and assume is between -π/2 and π/2. R 4 /³² 36 (d) R² - x² dx. (c) Using the trigonometric identity cos² 0 = (1 + cos(20)), we can rewrite the new integral as π/2 Evaluate this definite integral. √9 - x² dx. cos2 Ꮎ d0 = 18 3 ™1² 0 (1 + cos(20)) do. Did you find that the definite integral is 3²π = 9π, as expected?
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