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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.3 - Problem 32e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.3 - Problem 32e

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# Evaluate the following integrals. | Ch 7.3 - 32E

ISBN: 9780321570567 2

## Solution for problem 32E Chapter 7.3

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.

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

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