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Evaluate the following integrals. | Ch 7.3 - 32E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 32E Chapter 7.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 32E

Problem 32E

Evaluate the following integrals.

Step-by-Step Solution:

Problem 32E

Evaluate the following integrals.

                         dx.

Answer;

Step 1

          The given integral is  

         By  the substitution method we can evaluate the limit .

                     For our convenience  let , us take  x = 3 sin(p)  (or) x = 3 cos(p)

                       Let  x = 3 sin(p) , that implies  = sin(p) = , = cos(p) = , and tan(p) =  =  , cot (p)  = …………..(1)

   Then the integrand becomes =

         

                                                                 = , since = 9.

                                                                  =  

                                                                    = ,

                                                                                      since (p) += 1 , and  = 9.

                                                                   =  = cot(p) cosec(p) ,

                                                                                   since = cosec(p) , = cot(p)

                                  Therefore , if x = 3 sin(p) , then =  cot(p) cosec(p)………….(2)

                                         And    (x) = 3 cos(p)  ,  sin(x) = cos(x)

                                                      1 = 3 cos(p)

                                         That is , dx = 3 cos(p) dp…………….(3)

                       From (2) , (3) the above integral becomes ;

                                          = ( 3 cos(p)) dp

                                                               =  , since = cot(p).

                                                               =   , since -  = 1.

                                                               =  

                                                               = -cot(p) - p + c ,

                                                                       since   = Cx

                                                   = -( cot(p) + p) + C

                                                    = -(  +  )) +c ,

                                         since  cot (p)  =  ,  = sin(p) then p =  )

                                       Therefore ,     =  -(  +  )) +c

Step 2 of 1

Chapter 7.3, Problem 32E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Evaluate the following integrals. | Ch 7.3 - 32E