Can someone give me a run down on fundamental theorem? (1 Viewer)

[Kingportable]

Odd function is


even function is



The answer to this question


its negative four



which means i have the wrong understanding of it

So please teach me how to use the fundamental equation i am obviously confused on how to substitute the A's, as well how do you figure out algebraicly if its even or odd and what do you do if its neither. If you want to teach me reversing the integral, constant multiplier and sums of functions would be very much appreciated. Thank you.

 

[billybobneck]

you're a newbs son

does -0=-2?

 

[Kingportable]

WHAT THE HELL IS GOING ON! I seriously don't know how to use this formula! I can't seem to find it on maths online!!!!!!!!!!!!!

 

[Mature Lamb]

Note how the odd function is integrated from -a to a.

For the 2x, it's integrated from -2 to 0. For it to equal to 0, it should be integrated from -2 to 2 instead.

 

[Kingportable]

dy/dx=2x
y=x^2
from 2 to -2 = 4 - 4 = 0 times 2 = 0
WHICH IS NOT -4!!!!!

 

[Mature Lamb]

dy/dx=2x
y=x^2
from 2 to -2 = 4 - 4 = 0 times 2 = 0
WHICH IS NOT -4!!!!!

Yes because you integrated that odd function (2x) from -2 to 2 which produces 0.

 

[Kingportable]

we are looking for the area of 2x from -2 to 0, x^2 integrating this from -2 to 2 of -2 to 2 is all zero even if you multiply it by 2!

 

[Mature Lamb]

we are looking for the area of 2x from -2 to 0, x^2 integrating this from -2 to 2 of -2 to 2 is all zero even if you multiply it by 2!

Sounds like you're confusing yourself a bit mate.

You want the area of 2x from -2 to 0, then neither of those formulae you mentioned above will apply. You do it normally.

 

[Kingportable]

OK i will do this normally in LaTeX even than is -4 the text book says.

THE question is:
<a href="http://www.codecogs.com/eqnedit.php?latex=\int_{-2}^{0}2x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\int_{-2}^{0}2x" title="\int_{-2}^{0}2x" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{2}{(1@plus;1)}.2^{1@plus;1}@plus;C = x^2@plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{2}{(1+1)}.2^{1+1}+C = x^2+c" title="\frac{2}{(1+1)}.2^{1+1}+C = x^2+c" /></a>
<a href="http://www.codecogs.com/eqnedit.php?latex=(x^2)_{-2}^{0} =(0)^2-(-2)^2=0-(4)=-4" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(x^2)_{-2}^{0} =(0)^2-(-2)^2=0-(4)=-4" title="(x^2)_{-2}^{0} =(0)^2-(-2)^2=0-(4)=-4" /></a>

that is as slowly as i can humanly do it, ok... AND IF YOU HAVE BEEN TROLLING ME, fuck

 

[tohriffic]

A function is even if <img src="http://latex.codecogs.com/gif.latex?f(x) = f(-x)" title="f(x) = f(-x)" />

And it is odd if <img src="http://latex.codecogs.com/gif.latex?-f(x) = f(-x)" title="-f(x) = f(-x)" />

If it is neither, you don't do anything to the limits/boundaries.

I don't see anything wrong in doing that particular question normally.
As for the rest of your question, could you please clarify what you want to find out? It's a little confusing with how you're wording it.

 

[Kingportable]

I just want to use the fundamental theorem to answer the question, tohriffic

 

[Mature Lamb]

I just want to use the fundamental theorem to answer the question, tohriffic

You can't, that's the thing. And no, I promise I'm not trolling. See how the Fundamental Theorem SPECIFICALLY states you have to integrate from -a to a? Your question is integrating from -2 to 0. If -a = -2, then a = 2, which is not the 0 that's in your question.

HENCE, you can't use it for that question.

 

[D94]

2x is an odd function. You've integrated an odd function from -2 to 0. That means the given area is below the axis. When you integrate an odd function from -a to a, you will naturally get 0 as the answer. But you're only integrating from -2 to 0, NOT -2 to 2 (which would give 0). Since you are integrating from -2 to 0, the answer will be -4.

 

[Kingportable]

Sereiously? The text book told me to use the fundamental theorem. FUCK i've been obsession about this question for hours, i see that they just want us to reason our way out off using the formulas.

 

[Kingportable]

Seriously?? The text book told me to use the fundamental theorem. FUCK i've been obsession about this question for hours, i see that they just want us to reason our way out off using the formulas.

 

[Shadowdude]

You can't, that's the thing. And no, I promise I'm not trolling. See how the Fundamental Theorem SPECIFICALLY states you have to integrate from -a to a? Your question is integrating from -2 to 0. If -a = -2, then a = 2, which is not the 0 that's in your question.

HENCE, you can't use it for that question.

^ confirmed Advanced Maths student - knows what he's talking about. pls listen to him

 

[Kingportable]

You can't, that's the thing. And no, I promise I'm not trolling. See how the Fundamental Theorem SPECIFICALLY states you have to integrate from -a to a? Your question is integrating from -2 to 0. If -a = -2, then a = 2, which is not the 0 that's in your question.

HENCE, you can't use it for that question.

Seriously?? The text book told me to use the fundamental theorem. FUCK i've been obsessing about this question for hours, i see that they just want us to reason our way out off using the formulas. ANY WAY THANK YOU FOR CLARIFYING THIS GUYS, really thank you, i am sorry that i've been raging.

 

[SpiralFlex]

Meditate then integrate...

There is no need for violence, which book did you use?

 

[Kingportable]

cambridge 2u HSC, Chapter 1C Question 1a

 

[D94]

Seriously?? The text book told me to use the fundamental theorem. FUCK i've been obsession about this question for hours, i see that they just want us to reason our way out off using the formulas.

Ok, it's still possible to use the fundamental theorem: