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# Answer: Geometry problems Use a table of integrals to ISBN: 9780321570567 2

## Solution for problem 35E Chapter 7.5

Calculus: Early Transcendentals | 1st Edition

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Problem 35E

Geometry problems

Use a table of integrals to solve the following problems.

Find the length of the curve y = ex on the interval [0, ln 2].

Step-by-Step Solution:
Step 1 of 3

Problem 35E

Geometry problems  Use a table  of integrals  to solve the following problems.

Find the length of the curve  y= on the interval [0, ln(2)].

Step-1;

If is a continuous on [a,b] , then the length of the curve y = f(x) , a is

L =  dx.

If we use Leibniz notation for derivatives , we can write the  arc length formula as follows:

L =  dx.

Step-2

The given curve is   y = , and the interval is[0,ln(2)].

Now , we have to find out the length of the curve  y= on the interval [0,ln(2)].........(1)

If y = f(x) = , then (y) = f(x) =  ) = = ……………(2)

So , the arc length formula gives;

L =  dx =  dx.

Therefore , L =  dx  , since from(1) ,(2).

=  dx  , since = L =  dx  =  dx  ……….(3)

Step-3;

Consider , For our convenience  take substitution method: put 2 x =t , then differentiation of  2 x =t is ; (2x) = (dt/dx) dx= dt …………(4)

Therefore , = =  dt

Substitute  , +1 =  = = p, then the differentiation of +1 = is  +1) =   = 2p dt = dp

= dp , since +1 = …………..(5)

Therefore , the above integral becomes; =  dt  =  (p) dp

= Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

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Answer: Geometry problems Use a table of integrals to

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