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

1. anonymous

L = ∫ sqrt(1 + (dy/dx)^2) dx

2. anonymous

i dont get it maam

3. freckles

do you know what dy/dx means ?

4. anonymous

yes its the derivative

5. freckles

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

6. geerky42

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

7. anonymous

thanks sir

8. anonymous

thanks for the clearer explanation @geerky42