Intergration (1 Viewer)

[Lukybear]

How is the value of -8^(5/3)/5 found?

 

[Thecorey0]

I am assuming the function is x^(2/3). If so there is no solution, because it is not defined for x<0. Therefore you can not evaluate the integral from 8 to -8. That is unless I am missing something.

 

[Casper_18]

How is the value of -8^(5/3)/5 found?

when you do this you have to consider the graph. Seeing as though they are not asking for an area and what you are integrating is an even function. i.e. F(x) = F(-x) then it becomes:



so in your case



Hope this helps you

 

[kaz1]

I am assuming the function is x^(2/3). If so there is no solution, because it is not defined for x<0. Therefore you can not evaluate the integral from 8 to -8. That is unless I am missing something.

You can find the cube root of a negative number.

 

[Casper_18]

You can find the cube root of a negative number.

Correct and if you remember your index laws anyway x^(2/3) you are squaring and then taking the cube root so you are taking a positive cube root anyway. because any number squared is positive in the real number system.

 

[Aerath]

Why isn't x defined for x <0?

For instance, y = x^2. Does this mean that x cannot be -1?

[I think you mean y cannot be less than 0]

 

[Thecorey0]

Why isn't x defined for x <0?

For instance, y = x^2. Does this mean that x cannot be -1?

[I think you mean y cannot be less than 0]

I'm sorry, my mistake. I attempted the question and did not get the answer the poster asked for. So I entered the function on a graphing calculator, and simply observed that it only existed in the upper right quadrant.

 

[Lukybear]

It does seem you can take the cube root of a negative... But my calculator somehow, when I entered the -8^(5/3) gave me an error...

Any1 have any ideas about that? Is it because im using a sharp?

 

[Thecorey0]

Any1 have any ideas about that? Is it because im using a sharp?

I also use a sharp, and it too gives an error. One method would be to use your index laws and do ((-8)^1/3)^5.

 

[Lukybear]

Do you know why that happens? Is the casio calculators better?

 

[Thecorey0]

Do you know why that happens? Is the casio calculators better?

I have no idea why it happens. I have never used a casio - I have used the same calculator since year 7, so I am not one to comment on them.

 

[Iruka]

I believe some calculators find the cube root (or any other root) via an algorithm that takes logarithms first. That is why they are giving you a math error - you can't take the log of a negative number.

 

[Lukybear]

Thanks Iruka.

It just that I am worried, that using a sharp calculator will give me a slight disadvantage or something. I know such novelties shouldnt even be considered at my level but...

 

[Casper_18]

I have used the SHARP calculator since year 7, the exact same one. I dont Get math errors when I type in -8^(5/3)/5 though. The sharp calcuator is a very good calculator. Although I have found that Casio are better at calculating fractions of larger decimals.