Question

find the length of the graph of the function x=0 to x=2
f(x) = sqrt(x^3)

Answer 1

\[f(x) = \sqrt{x^{3}}\]

Answer 2

Find the 2 y values using x=0 to x=2, then use distance formula

Answer 3

how do i set that up after I find y values... I don't know the distance form of the top of my head

Answer 4

and I got 0 and sqrt of 8 for th y values

Answer 5

But if you want the length of this quadratic you need to use calculus

Answer 6

ok help me out cause I am lost

Answer 7

you need to integrate
\[\int\limits_0^2 \sqrt{1+\frac{9 x}{4}} \, dx\]

Answer 8

and that is it

Answer 9

yes the answer should be 3.52552

Answer 10

ok thanks I will try and get that

Answer 11

i got that but negative

Answer 12

\[\begin{array}{l} \text{For the integrand }\sqrt{\frac{9 x}{4}+1}\text{, substitute }u=\frac{9 x}{4}+1\text{ and }du=\frac{9}{4}d x: \\ \text{}=\frac{4}{9}\int\limits \sqrt{u} \, du \\ \text{The integral of }\sqrt{u}\text{ is }\frac{2 u^{3/2}}{3}: \\ \text{}=\frac{8 u^{3/2}}{27} \\ \text{Substitute back for }u=\frac{9 x}{4}+1: \\ \text{}=\frac{1}{27} (9 x+4)^{3/2} \\\end{array}\]

Answer 13

ok only question left is why 9x and 4 where did you use the y values we found

Answer 14

oh those are from the formula

\[arc length=\int\limits_{a}^{b}\sqrt{1+(f~'[x])^2}dx\]
where a is the initial point and b is the final point

Answer 15

ok thanks for all the help you were great

Answer 16

be aware its (f ' (x))^2
so from
\[\sqrt{x}^3\]
x^3/2
differentiate
\[f~'(x)=\frac{3}{2}x^{1/2}\]