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anonymous
 one year ago
integral calculus:
determine the length of the arc of the curve y=e^x from x=0 to x=1?
anonymous
 one year ago
integral calculus: determine the length of the arc of the curve y=e^x from x=0 to x=1?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0L = ∫ sqrt(1 + (dy/dx)^2) dx

freckles
 one year ago
Best ResponseYou've already chosen the best response.0do you know what dy/dx means ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes its the derivative

freckles
 one year ago
Best ResponseYou've already chosen the best response.0ok well as you can see the formula needs you to calculate that

geerky42
 one year ago
Best ResponseYou've already chosen the best response.2To find length of arc, you use this: \[\int\sqrt{1+\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2}\mathrm dx\] Here, we have \(y = e^x\) Obviously, \(\dfrac{\mathrm dy}{\mathrm dx} = e^x\) So you have to evaluate \[\int\sqrt{1+\left(e^x\right)^2}\mathrm dx = \int\sqrt{1+e^{2x}}\mathrm dx \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks for the clearer explanation @geerky42
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