# Thread: Integral - Pls check my work

1. ## Integral - Pls check my work

$\displaystyle \int_{-1}^{1} (\sqrt[3]{u} + 1)^{2} du$

This is what I did:
(FOIL)
$\displaystyle \int_{-1}^{1} ({u}^{2/3} + 2u^{1/3} + 1) du$

$\displaystyle \left[ \frac{3}{5}u^{5/3} + \frac{3}{2}u^{4/3} + u + C\right]_{-1}^{1}$

$\displaystyle \frac{3}{5}(1)^{5/3} + \frac{3}{2}(1)^{4/3} + 1 + C - \left(\frac{3}{5}(-1)^{5/3} + \frac{3}{2}(-1)^{4/3} - 1 + C \right)$

$\displaystyle \frac{3}{5} + 1 + \frac{3}{5} + 1$

$\displaystyle \frac{16}{5}$

But when I check it here: Function calculator it gives me what appears to be an imaginary number, it says the answer is: $\displaystyle 4.53546396068 + 1.80971485451I_{3}$. But I can't understand why, the negative ones should all work because they are never taken to an even root.

2. Originally Posted by angel.white
$\displaystyle \int_{-1}^{1} (\sqrt[3]{u} + 1)^{2} du$

This is what I did:
(FOIL)
$\displaystyle \int_{-1}^{1} ({u}^{2/3} + 2u^{1/3} + 1) du$

$\displaystyle \left[ \frac{3}{5}u^{5/3} + \frac{3}{2}u^{4/3} + u + C\right]_{-1}^{1}$

$\displaystyle \frac{3}{5}(1)^{5/3} + \frac{3}{2}(1)^{4/3} + 1 + C - \left(\frac{3}{5}(-1)^{5/3} + \frac{3}{2}(-1)^{4/3} - 1 + C \right)$

$\displaystyle \frac{3}{5} + 1 + \frac{3}{5} + 1$

$\displaystyle \frac{16}{5}$

But when I check it here: Function calculator it gives me what appears to be an imaginary number, it says the answer is: $\displaystyle 4.53546396068 + 1.80971485451I_{3}$. But I can't understand why, the negative ones should all work because they are never taken to an even root.
Funny. It told me that $\displaystyle (u^{1/3} + 1)^2$ didn't exist on the whole interval.

I guess the solution is that Function calculator sucks.

-Dan

3. Originally Posted by topsquark
Funny. It told me that $\displaystyle (u^{1/3} + 1)^2$ didn't exist on the whole interval.

I guess the solution is that Function calculator sucks.

-Dan
did you try evaluating the second part of his answer in a regular calculator?

maple gave me a complex answer as well, i can't see why at the moment

4. Originally Posted by Jhevon
did you try evaluating the second part of his answer in a regular calculator?

maple gave me a complex answer as well, i can't see why at the moment
I looked at his solution (and found no errors) and after seeing how bad the function calculator was, I ran it through my TI-92.

My guess is that the programs are having trouble with the cube root for negative x. (Though you would think that Maple at least wouldn't have that problem.)

-Dan

5. Originally Posted by topsquark
I looked at his solution (and found no errors) and after seeing how bad the function calculator was, I ran it through my TI-92.

My guess is that the programs are having trouble with the cube root for negative x. (Though you would think that Maple at least wouldn't have that problem.)

-Dan
which brings up another interesting--maybe related--point. when you try to graph x^(1/3) with Graph, it only graphs the function for positive x's. why is it that programs have trouble evaluating the odd roots of negative numbers? is it a glich, or do they know something that we don't?

6. Mine works perfectly fine for negative x

7. Originally Posted by DivideBy0
Mine works perfectly fine for negative x
Which do you use? & is it free?

8. Originally Posted by angel.white
Which do you use? & is it free?
Graph is free, and it works great (except, perhaps, in this situation ). do you have it?

9. Originally Posted by Jhevon
Graph is free, and it works great (except, perhaps, in this situation ). do you have it?

I've been using:
Cool math .com - Online Graphing Calculator - Graph It!
and Function Grapher Online

10. Originally Posted by angel.white

I've been using:
Cool math .com - Online Graphing Calculator - Graph It!
and Function Grapher Online
well, Graph does a lot more than just plot graphs. it does other cool things, like finding the area under curves and stuff

11. Originally Posted by Jhevon
Graph is free, and it works great (except, perhaps, in this situation ). do you have it?
Wow, it's a pretty neat program I like how easy it is to check an answer, click the shady parabola thing :P

But, it also could not verify the answer for negative numbers, said it was imaginary. But I checked my answer anyway by taking it from 0 to 1 instead, and graph agreed with me, so if I got it wrong, then it's only due to an arithmetic error at the end. And that is rather unlikely as topsquark got the same answer.

On a side note, I wish I was a robot.

12. Originally Posted by Jhevon
well, Graph does a lot more than just plot graphs. it does other cool things, like finding the area under curves and stuff
And make smiley faces.

13. (Someone has a lot of spare time on their hands!)

-Dan