Integrate the following, definite integral

• Jul 29th 2011, 01:00 PM
Integrate the following, definite integral
Attached is the problem that I can't solve.
Can some one look at it and tell me what I am doing wrong?

Did I do the antiderivative correct also??

This is where I F(b) - F(a) to get my answer.

DISREGARD the bottom statement on the sheet, where I sent it to my teacher to help me, if he replies.

Thanks.
Joanne
• Jul 29th 2011, 01:02 PM
Siron
Re: Integrate the following, definite integral
There's nothing to see ...
• Jul 29th 2011, 01:02 PM
TheChaz
Re: Integrate the following, definite integral
Attached - ???
(I can't see anything... maybe it's just me!)
• Jul 29th 2011, 01:16 PM
Siron
Re: Integrate the following, definite integral
There's a mistake in the second step, it has to be:
$\int_{-4}^{-1} \left(\frac{2}{x^{\frac{4}{5}}}-\frac{x^{\frac{2}{3}}}{5}\right)dx$
$=2\int_{-4}^{-1}x^{\frac{-4}{5}}dx -\frac{1}{5}\int_{-4}^{-1}x^{\frac{2}{3}}dx$
...
• Jul 29th 2011, 01:23 PM
Re: Integrate the following, definite integral
Siron,
The first fraction of x is suppose to be x^ 2/5.
OK so is this correct?

10/7(1/x^7/5) - 3/25(x)^5/3 ??
But when I key in -4 and -1 for x, I will get an error.

I heard you do something with the negatives on the limits?? perhaps?
Is my antiderivative correct? and how do you get around the error of this?

Thanks
• Jul 29th 2011, 01:30 PM
e^(i*pi)
Re: Integrate the following, definite integral
$-4^{3/5}$ is definitely real. It's about -2.3

$\left(\dfrac{10}{3}(-1)^{2/5} - 3(-1)^{5/3}\right) - \left(\dfrac{10}{3}(-4)^{2/5} - 3(-4)^{5/3}\right)$

IIRC you can switch around the limits but only if you take the negative of the whole integral: that is $\int^a_b = -\int^b_a$
• Jul 29th 2011, 01:31 PM
Re: Integrate the following, definite integral
So remove the negatives on both numbers and put the negative outside the integral sign?

So the -2.3 above, you basically do the calculation leaving out the (-) sign and then add it after???
• Jul 29th 2011, 01:33 PM
Siron
Re: Integrate the following, definite integral
Sorry, I read -4/5 for the exponent.
My calculator says: $(-4)^{\frac{3}{5}}=-2,2979...$
• Jul 29th 2011, 01:40 PM
Re: Integrate the following, definite integral
Siron, how do you do that calculation. I keyed in exactly what you have there and I get an error? Is there something I am missing to calculate this?
I am not seeing this for some reason. Is it because the root is odd, it's going to be a negative number?? as the root is 5??
• Jul 29th 2011, 01:44 PM
e^(i*pi)
Re: Integrate the following, definite integral
These are the keys I used
Code:

( - 4 ) ^ (3 / 5 )
Ultimately though $(-4)^{3/5} = \sqrt[5]{(-4)^3} = \sqrt[5]{-64}$. Since the exponent is odd this should give a real number.
• Jul 29th 2011, 01:45 PM
Siron
Re: Integrate the following, definite integral
Which calculator do you have? Ti-83? Notice there are two '-' signs, one that indicates a negative number and one that indicates the operation the 'difference between to numbers', you have to use the one that indicates negative numbers.
• Jul 30th 2011, 01:47 AM
HallsofIvy
Re: Integrate the following, definite integral
Just a few comments to add: an odd root of a negative number, or the fractional power of a negative number, where the denominator of the fractional power is odd is NOT an imaginary number! For n odd, $(-a)^{m/n}= -(a^{m/n})$. Some (but not all) calculators do roots by taking logarithms which will not give correct answers for negative arguments. Really good calculators should be able to handle the "odd root of a negative power" but not all do.

And, finally, $\int_{-4}^{-1} f(x)dx$ and $\int_{-1}^{-4} f(x)dx$ are NOT the "same thing". One is the negative of the other: $\int_{-4}^{-1} f(x)dx= -\int_{-1}^{-4} f(x)dx$.
• Jul 30th 2011, 06:27 AM