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Numerade Educator

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Problem 31 Easy Difficulty

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) $.

Answer

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

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Video Transcript

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.