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## Homework Statement

Use the integration tables to find the exact arc length of the curve

f(x)=ln x 1≤x≤e

Reference the table number formula used

Then approx. your answer and compare that to the approx. "straight line distance" between 2 points

coordinates of two points (1,0) (e,1)

## Homework Equations

∫sqrt(1+(f'(x))^2)

distance formula I'm guessing?

## The Attempt at a Solution

y = ln(x)

y' = (1/x)

L = ∫ (1 to e) [ sqrt(1 + (1/x)^2) ] dx

L = ∫ (1 to e) [ sqrt(1 + (1/x)^2) ] dx

= ∫(1 to e) [ sqrt(1 + (1/x^2)) ] dx

= ∫ (1 to e) [ sqrt( (x^2 + 1) / x^2) ) ] dx

=∫ (1 to e) [(1/x)*sqrt(x^2 + 1) ] dx

Integral # 28

∫ [(1/u)sqrt(a^2 + u^2)] du

= sqrt(a^2 + u^2) - a*ln | [a + sqrt(a^2 + u^2)] / u] | + C

In this integral, a = 1 and u = x

Int (1 to e) [(1/x)*sqrt(x^2 + 1) ] dx =

sqrt(1 + x^2) - ln | [1 + sqrt(1 + x^2)] / x] | (1 to e)

=

sqrt(1 + e^2) - ln | [1 + sqrt(1 + e^2)] / e] |

=

sqrt(2) - ln | [1 + sqrt(2)]] |

0.53

straight line =1.98

Is this right?