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

$l=\int\limits^a_b {\sqrt{1+(x')^2} \, dy$

x' is the derivative with respect to y

Given value of x is

$x = y^{1/2}$

Differentiating with respet to y

$x ' = \frac{1}{2y^{1/2}}$

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

$L=\int\limits^4_0 { \sqrt{1+\frac{1}{4y}}} \, dy$

$L = 4.65$