Question

Find the length of the curve on the given interval x=y^(1/2) from y=0 to y=4

Answer 1

Here we have to use the following formula

`l=\int\limits^a_b {√(1+(x')^2) \, dy`

x' is the derivative with respect to y

Given value of x is

`x = y^(1/2)`

Differentiating with respet to y

`x ' = (1)/(2y^(1/2))`

Substituting the value of x' in the formula, we will get

`L=\int\limits^4_0 { \sqrt{1+(1)/(4y)}} \, dy`

`L = 4.65`