Integration (1 Viewer)

[artosis]

Strangely, the answer is false.

Since the function is even, shouldn't the answer be true?

 

[SpiralFlex]

Sketch the graph. For the second integral form you can't take the lower boundary as . Since there are vertical asymptotes at and . Hence the answer is false.

 

[Omnipotence]

Yeah, test whether it is even or not. In this case, it is even, so the rule satisfies.

 

[blackops23]

wierd question, do you mind posting the solution

 

[SpiralFlex]

*Points at Spiral's answer*

 

[artosis]

Yeah, test whether it is even or not. In this case, it is even, so the rule satisfies.

That's what I thought. But the rule doesn't satisfy this question.
SpiralFlex seemed to have gotten the answer. Am I really suppose to sketch a graph each time before changing the limits?

wierd question, do you mind posting the solution

Done.

 

[Tasteless]

Hi.

 

[SpiralFlex]

Hi.

Hi?

That's what I thought. But the rule doesn't satisfy this question.
SpiralFlex seemed to have gotten the answer. Am I really suppose to sketch a graph each time before changing the limits?



Done.

Graphically is the only safest method I know or maybe a HSCer will tell you another method.

What about this?





For real values of ,

Hence,





, [Since , ]

Hence the boundaries of the integral does not satisfy the domain.

 

[khfreakau]

Spiral is correct. Keep in mind the even function rule only applies if the function is CONTINUOUS across all values within limits. You can't say undefined = undefined, there's no such thing

 

[SpiralFlex]

Spiral is correct. Keep in mind the even function rule only applies if the function is CONTINUOUS across all values within limits. You can't say undefined = undefined, there's no such thing

Can you also check my method on top? I am not sure if it's theoretically correct. I just thought of it on the spot.

 

[xV1P3R]

I think it would be enough if you said:

4x² - 1 > 0
x² > 0.25
x > 0.5, x < -0.5
Curve is undefined for x between 0.5 and -0.5, therefore integral doesn't exist

ie. pretty much what the answer says.

@Spiralflex, you're making it more complicated than it should be.

 

[SpiralFlex]

I think it would be enough if you said:

4x² - 1 > 0
x² > 0.25
x > 0.5, x < -0.5
Curve is undefined for x between 0.5 and -0.5, therefore integral doesn't exist

ie. pretty much what the answer says.

@Spiralflex, you're making it more complicated than it should be.

Okay. Thanks, I will use your method once I reach Extension 2.

 

[K4M1N3]

Okay. Thanks, I will use your method once I reach Extension 2.

Oh damn. Do I sense a hint of "OH SNAPPERY" sarcasm?

 

[SpiralFlex]

Oh damn. Do I sense a hint of "OH SNAPPERY" sarcasm?

I don't get it? No I was being serious. I didn't see that method. Viper saved me time and potential marks in the HSC. Hence he was repped.

 

[K4M1N3]

Oh lol :S it sounded like you were being a smart ass cos you could answer an Ext2 question without doing ext2.....but nvm.

 

[SpiralFlex]

Oh lol :S it sounded like you were being a smart ass cos you could answer an Ext2 question without doing ext2.....but nvm.

I do not disrespect others. Unlike humans.

 

[LittlePetal316]

what in the weird is this. glad i don't do it.