# How do you find the length of the curve for #y=x^2# for (0, 3)?

##### 1 Answer

Nov 3, 2016

Arc Length

#### Explanation:

The Arc Length

With

# l = int_0^3 sqrt(1+(2x)^2)dx #

# :. l = int_0^3 sqrt(1+4x^2)dx #

I will quote the result, but if you want to see how to perform the integration, please use this link

# l = [sinh^-1(2x)/4 + (xsqrt(4x^2+1))/2]_0^3 #

# :. l = (sinh^-1 6/4 + (3sqrt(36+1))/2) - (sinh^-1 0/4 + 0)#

# :. l = (sinh^-1 6/4 + (3sqrt(37))/2) - (0 + 0)#

# :. l = 1/4sinh^-1 6 + 3/2sqrt(37)#