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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

##### ISBN: 9780321570567

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