Question

Find the arc length of the graph of the function f(x)=5 \sqrt{x^{3}} from x= 5 to x=6

Answer 1

so i know the arclength formula is \[\int\limits_{5}^{6}\sqrt{1+f'(x)^2}\]

Answer 2

and f(x)=5x^(3/2) f'(x)=\[15/2\sqrt{x}\]

Answer 3

i get to \[\int\limits_{5}^{6}\sqrt{1+225/4(x)}dx\]

Answer 4

do a substitution on the inside of the sqrt
u=1+225x/4

Answer 5

du=225/4dx?

Answer 6

yep
4du/225=dx

Answer 7

Don't forget to change the limits too.

Answer 8

then you evaluate your a and b with u

Answer 9

\[\frac{4}{225} \int\limits_{1+\frac{225(5)}{4}}^{1+\frac{225(6)}{4}}\sqrt{u} du\]

Answer 10

does it then go to \[4/225\int\limits_{282.25}^{338.5}\sqrt{u}du\]

Answer 11

to\[4/225(2u ^{3/2}/3)\left| \right|\]

Answer 12

from a->b

Answer 13

last part is to plug in and subtract

Answer 14

thanks