Finding the Length of y = x^{3/2} from x = 0 to x = 4

[Precursor]

Homework Statement

Find the length of the curve. y = x^{3/2} from x = 0 to x = 4.

Homework Equations

L = \int^{b}_{a} \sqrt{1 + (dy/dx)^{2}} dx

The Attempt at a Solution

L = \int^{b}_{a} \sqrt{1 + (dy/dx)^{2}} dx
L = \int^{4}_{0} \sqrt{1 + (3x^{1/2}/2)^{2}} dx
.
.
.
.
I used substitution rule
.
.
.
L = 64/27

Is this correct?

Thanks

 

[Ratio Test =)]

Homework Statement

Find the length of the curve. y = x^{3/2} from x = 0 to x = 4.

Homework Equations

L = \int^{b}_{a} \sqrt{1 + (dy/dx)^{2}} dx

The Attempt at a Solution

L = \int^{b}_{a} \sqrt{1 + (dy/dx)^{2}} dx
L = \int^{4}_{0} \sqrt{1 + (3x^{1/2}/2)^{2}} dx
.
.
.
.
I used substitution rule
.
.
.
L = 64/27

Is this correct?

Thanks

http://www.wolframalpha.com/input/?i=integrate+sqrt[+1+++[+(3/2)+x^(1/2)+]^2+]+from+x=0+to+x=4
Its better to post all of your work.

 

[Precursor]

http://www.wolframalpha.com/input/?i=integrate+sqrt[+1+++[+(3/2)+x^(1/2)+]^2+]+from+x=0+to+x=4
Its better to post all of your work.

So my answer is wrong afterall?

By the way, thanks a lot for that website! If only I knew such a website existed before.

 

[Ratio Test =)]

So my answer is wrong afterall?

By the way, thanks a lot for that website! If only I knew such a website existed before.

Yeah Its wrong.

You will face: \int_0^4 \sqrt{ 1 + \frac{9}{4}x } \;\ dx
What did you do for it?

 

[CompuChip]

Actually I found c(7 \sqrt{7} - 1),
where c is a numerical factor (I got 2/3) which I'm not sure of because I did the calculation sloppily.
So I suggest you show the rest of the calculation as well.

[edit] Too slow, you already have several replies. [/edit]

 

[Precursor]

Yeah Its wrong.

You will face: \int_0^4 \sqrt{ 1 + \frac{9}{4}x } \;\ dx
What did you do for it?

That's exactly what I got, but when I used the substitution rule, to integrate, I did not change the limits of integration to in terms of u.

 

[Ratio Test =)]

That's exactly what I got, but when I used the substitution rule, to integrate, I did not change the limits of integration to in terms of u.

Ohhh.
BTW, Its a famous mistake. :)