# How do you find the length of the curve for #y=x^(3/2) # for (0,6)?

##### 2 Answers

See below.

#### Explanation:

We need

# = 4/9 [2/3(1+(9x)/4)^(3/2)]_0^6#

# = 8/27[(4+9x)^(3/2)/8]_0^6#

# = 1/27(58sqrt58 - 8)#

16.064 (to 3 places of decimals)

#### Explanation:

Denoting some short segment of the curve by

Extracting

Taking square roots of both sides

from which

Now noting

implies

so

that is

so the required solution is

Gritting teeth and going for integration by substitution with

so that

from which

and noting required limits under the substitution

so

that is