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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

Re: Integrate the following, definite integral

There's nothing to see ...

Re: Integrate the following, definite integral

Attached - ???

(I can't see anything... maybe it's just me!)

Re: Integrate the following, definite integral

There's a mistake in the second step, it has to be:

$\displaystyle \int_{-4}^{-1} \left(\frac{2}{x^{\frac{4}{5}}}-\frac{x^{\frac{2}{3}}}{5}\right)dx$

$\displaystyle =2\int_{-4}^{-1}x^{\frac{-4}{5}}dx -\frac{1}{5}\int_{-4}^{-1}x^{\frac{2}{3}}dx$

...

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

Re: Integrate the following, definite integral

$\displaystyle -4^{3/5}$ is definitely real. It's about -2.3

$\displaystyle \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 $\displaystyle \int^a_b = -\int^b_a$

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???

Re: Integrate the following, definite integral

Sorry, I read -4/5 for the exponent.

My calculator says: $\displaystyle (-4)^{\frac{3}{5}}=-2,2979...$

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??

Re: Integrate the following, definite integral

These are the keys I used Ultimately though $\displaystyle (-4)^{3/5} = \sqrt[5]{(-4)^3} = \sqrt[5]{-64}$. Since the exponent is odd this should give a real number.

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.

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, $\displaystyle (-a)^{m/n}= -(a^{m/n})$. 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, $\displaystyle \int_{-4}^{-1} f(x)dx$ and $\displaystyle \int_{-1}^{-4} f(x)dx$ are NOT the "same thing". One is the negative of the other: $\displaystyle \int_{-4}^{-1} f(x)dx= -\int_{-1}^{-4} f(x)dx$.

Re: Integrate the following, definite integral

HI EVERYONE, thanks for all the help. There was something I was not getting and now you have helped me. I go an answer of 3.2351. I had to key in information into my calculator a different way for it to work. I don't have a graphing calculator yet. This week I will tho.

So to HallsofIvy, when you pull out the - and switch a and b. When does this get done? I know you add the negative to the equation, but has to happen to do this???

THanks again