# How do you find the lengths of the curve #y=(4/5)x^(5/4)# for #0<=x<=1#?

##### 2 Answers

#### Explanation:

We Need the formula

given

using that

to calculate the indefinite integtral we Substitute

so

and we have

this is

and we have

This is where the formula that is in Sonnhard's solution comes from.

#### Explanation:

Set the total length of the curve

Let us consider a minuscule portion of the curve that is so short and greatly magnified that it looks as though it is straight.

Set its length as

Using Pythagoras we have

Take the square root of both sides

Multiply by 1 and you do not change the value. However 1 comes in many forms.

But

Multiply

Sum up all the

As in Sonnhard's solution