# Integration - Dr. Evil is my teacher

• Nov 9th 2009, 11:32 AM
Silent Soliloquy
Integration - Dr. Evil is my teacher
Right I won't bore you with a sob story but this is a regular grade 12 class and we've been posed with this problem:

Find the arc length of this function across 0 -> 5:

$s(t) = t^3 - 6t^2 + 9t + 5, {t >= 0}$

I learned the formula of s = Integral of $squareroot(1+f'(x)^2) * dx$

So I began using the Riemann sums until I get here, I'm not quite sure how to proceed.

http://img26.imageshack.us/img26/6931/formulaz.jpg

If need be I will show how I got up to there, it just takes forever to use LaTeX.

PS: That should be x->infinity

Thanks!
• Nov 9th 2009, 11:46 AM
Quote:

Originally Posted by Silent Soliloquy
Right I won't bore you with a sob story but this is a regular grade 12 class and we've been posed with this problem:

Find the arc length of this function across 0 -> 5:

$s(t) = t^3 - 6t^2 + 9t + 5, {t >= 0}$

I learned the formula of s = Integral of $squareroot(1+f'(x)^2) * dx$

So I began using the Riemann sums until I get here, I'm not quite sure how to proceed.

http://img26.imageshack.us/img26/6931/formulaz.jpg

If need be I will show how I got up to there, it just takes forever to use LaTeX.

PS: That should be x->infinity

Thanks!

I don't see why you're trying to calculate the limit of the Riemann sum when you have the formula. That will be difficult. Why don't you just use the formula?
• Nov 9th 2009, 11:54 AM
Silent Soliloquy
Quote:

I don't see why you're trying to calculate the limit of the Riemann sum when you have the formula. That will be difficult. Why don't you just use the formula?

Hm, I thought the Reimann sum was a way to find the integral. Oddly enough we never did integrals so I had to scour what I could from textbooks and the internet.

Is the integral

$\frac{2}{3} (x+3(x^{2}-4x+3)^3)^\frac{3}{2}$

for the function

$(1+9(x^{2}-4x+3)^2)^\frac{1}{2}$

Thanks, sorry about all the trivial trouble.
• Nov 9th 2009, 01:27 PM
Quote:

Originally Posted by Silent Soliloquy
Hm, I thought the Reimann sum was a way to find the integral. It is one way, but they can be very difficult to evaluate. It's much like using the first principles to find a derivative. You can use the limit formula if you want, but it's just not something people often do since it just makes it too difficult. However, in your case it's really difficult to use the formula too.Oddly enough we never did integrals so I had to scour what I could from textbooks and the internet. That's pretty wierd, this topic isn't discussed until page 563 of my University Calculus text book. I think this is a Calc II topic.

Is the integral

$\frac{2}{3} (x+3(x^{2}-4x+3)^3)^\frac{3}{2}$

for the function

$(1+9(x^{2}-4x+3)^2)^\frac{1}{2}$

Thanks, sorry about all the trivial trouble.

No, this integral seems difficult to solve. I will start a new thread to see if anyone else can help. I'm afraid people may ignore your post since I responded to it. The integral you have to evaluate looks like this:

$\int_0^5\sqrt{1+(3t^2-12t+9)^2}dt$

I'm not sure if this is something that is practical to solve by hand. I will start a thread with this integral to see what
others say.

• Nov 9th 2009, 02:04 PM
Silent Soliloquy
Quote:

$\int_0^5\sqrt{1+(3t^2-12t+9)^2}dt$