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Use either a computer algebra system or a table of integrals to find the $ exact $ length of the arc of the curve $ y = e^x $ that lies between the points $ (0, 1) $ and $ (2, e^2) $.

$L=-\sqrt{2}+\sqrt{1+e^{4}}+\tanh ^{-1} \sqrt{2}-\tanh ^{-1} \sqrt{1+e^{4}}$

Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 1

Arc Length

Applications of Integration

Campbell University

Oregon State University

Harvey Mudd College

Lectures

01:11

In mathematics, integratio…

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01:59

Use either a computer alge…

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09:38

01:49

Find the arc length of the…

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02:47

Find the exact arc length …

05:01

Use the arc length formula…

16:59

Calculate the arc length o…

01:31

Set up an integral that re…

units. We're selling you right here, so we have to find a link that occur for why is equal to eat. The X on access between zero and two included, so are derivative because this e to the X So using our darkling formula, we just plug it in since from 0 to 2 square root of one plus eat the X square T X in the skin says negative square root of two plus square root of one plus each. The four plus the hyperbolic function of 10 in verse square root to minus the hyperbolic function of 10 in verse square root of one plus need to the fore power.

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