Question

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

Answer 1

L = ∫ sqrt(1 + (dy/dx)^2) dx

Answer 2

i dont get it maam

Answer 3

do you know what dy/dx means ?

Answer 4

yes its the derivative

Answer 5

ok well as you can see the formula needs you to calculate that

Answer 6

To 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 \[\int\sqrt{1+\left(e^x\right)^2}\mathrm dx = \int\sqrt{1+e^{2x}}\mathrm dx \]

Answer 7

thanks sir

Answer 8

thanks for the clearer explanation @geerky42