Question

Find the length of the curve.

y = 2x3/2 between x = 0 to x = 5/4

Answer 1

use

\[\int\limits_{a}^{b}\sqrt{1+(f'(x))^2}dx\]

Answer 2

nice latex. did you finish? it always is cooked up so the square of the derivative is something nice

Answer 3

\[f(x)=2x^{\frac{3}{2}}\]
\[f'(x)=3x^{\frac{1}{2}}\]
\[(f'(x)^2=9x\] so you need
\[\int_0^{\frac{5}{4}} \sqrt{1+9x}\]

Answer 4

ya, i did the same, square root of 1+9x . but the answer is not the same.

Answer 5

antiderivative is
\[\frac{2}{27}\sqrt{(1+9x)^2}\] yes?

Answer 6

2/9*3*square root of 1+9x . is it true?

Answer 7

think your off here.

Answer 8

no,. mine is different.
square root of 1+9x is at the bottom.

Answer 9

you have a choice. use
\[u=1+9x\]
\[\frac{1}{9}du=dx\] get
\[\frac{1}{9}\int u^{\frac{1}{2}} du=\frac{2}{3}\times \frac{1}{9}u^{\frac{3}{2}}\]

Answer 10

you want ANTI - DERIVATIVE. looks like you are taking the derivative.

Answer 11

add one to the exponent and then multiply by the reciprocal.
\[\frac{1}{2}+1=\frac{3}{2}\]

Answer 12

got it. thanks