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May 22, 2025, 04:19:05 am
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Author Topic: What would you say this integral equals? (VCE students only)  (Read 2818 times)  Share 

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QuantumJG

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What would you say this integral equals? (VCE students only)
« on: November 05, 2012, 06:01:55 pm »
+1
Evaluate:



I'm looking forward to what people say, since it was an exam question for year 11 students at my old school.

Edit: Sorry about forgetting those details.
« Last Edit: November 05, 2012, 06:13:58 pm by QuantumJG »
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Nobby

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Re: What would you say this integral equals? (VCE students only)
« Reply #1 on: November 05, 2012, 06:06:16 pm »
0
6 ?
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Lasercookie

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Re: What would you say this integral equals? (VCE students only)
« Reply #2 on: November 05, 2012, 06:12:01 pm »
+1
Where is the dx meant to go?

Did you mean

(integral minus 1/x^2)

or


(the 1/x^2 also inside the integral)

I'm guessing it's the second one, but just want to clarify
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b^3

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Re: What would you say this integral equals? (VCE students only)
« Reply #3 on: November 05, 2012, 06:13:17 pm »
+7
So tempted to post sol.... must hold back..... :P
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abeybaby

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Re: What would you say this integral equals? (VCE students only)
« Reply #4 on: November 05, 2012, 06:14:30 pm »
+1
i did vce in 2010, am i allowed to answer?
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Homer

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Re: What would you say this integral equals? (VCE students only)
« Reply #5 on: November 05, 2012, 06:15:46 pm »
+3
wouldn't it be infinity since there is an asymptote at y=0
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QuantumJG

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Re: What would you say this integral equals? (VCE students only)
« Reply #6 on: November 05, 2012, 06:28:08 pm »
0
Quote from: babes22 on November 05, 2012, 06:14:30 pm
i did vce in 2010, am i allowed to answer?

You're doing biomedicine so yes.

Quote from: Jai on November 05, 2012, 06:15:46 pm
wouldn't it be infinity since there is an asymptote at y=0

Yep. The reason why I asked this, is that some students would just naively integrate and evaluate the function at the terminals.
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pi

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Re: What would you say this integral equals? (VCE students only)
« Reply #7 on: November 05, 2012, 06:30:08 pm »
+1
Did VCE last year and doing no maths in uni, but I'm pretty sure that q shouldn't be on a yr11 test haha. Area is -infinity as the integral doesn't converge?


edit: sloppy wording, oops
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Homer

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Re: What would you say this integral equals? (VCE students only)
« Reply #8 on: November 05, 2012, 06:31:17 pm »
+2
WOOHOO!
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Jenny_2108

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Re: What would you say this integral equals? (VCE students only)
« Reply #9 on: November 05, 2012, 06:39:05 pm »
+1
Quote from: QuantumJG on November 05, 2012, 06:28:08 pm
Quote from: Jai on November 05, 2012, 06:15:46 pm
wouldn't it be infinity since there is an asymptote at y=0

Yep.

WOT? It should be vertical asymptote at x=0, not y

Quote from: ρнуѕικѕ ♥ on November 05, 2012, 06:30:08 pm
Did VCE last year and doing no maths in uni, but I'm pretty sure that q shouldn't be on a yr11 test haha. Area is -infinity as the integral doesn't converge?

Yeah, I agree. This is improper integral and the integrand is unbounded, which isn't in yr 11 course. Its unfair for yr 11 students imo
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Homer

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Re: What would you say this integral equals? (VCE students only)
« Reply #10 on: November 05, 2012, 06:40:42 pm »
+1
oh yeah, well thats what i meant haha :/
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abeybaby

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Re: What would you say this integral equals? (VCE students only)
« Reply #11 on: November 05, 2012, 06:42:05 pm »
+1
Afaik, the integral doesn't exist because it doesn't converge.
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Jenny_2108

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Re: What would you say this integral equals? (VCE students only)
« Reply #12 on: November 05, 2012, 06:48:19 pm »
+1
Quote from: babes22 on November 05, 2012, 06:42:05 pm
Afaik, the integral doesn't exist because it doesn't converge.

so if the integral gives result infinity, it means the integral doesn't exist?
The CAS gives result as negative infinity btw
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Homer

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Re: What would you say this integral equals? (VCE students only)
« Reply #13 on: November 05, 2012, 06:51:00 pm »
+1
wouldn't it be positive infinity since you times it with -1 as it is under the x-axis?
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KevinooBz

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Re: What would you say this integral equals? (VCE students only)
« Reply #14 on: November 05, 2012, 07:03:37 pm »
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Quote from: Jai on November 05, 2012, 06:51:00 pm
wouldn't it be positive infinity since you times it with -1 as it is under the x-axis?
It's a negative equation of a truncus I believe, so integrating the equation would result in most of the area being below the x axis.
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