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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

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Answer: Geometry problems Use a table of integrals to

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