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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,161

The area of the region

, , Y-axis, and the line x = 3 is ....A. 16 unit area

B. 18 unit area

C. unit area

D. 64 unit area

E. 72 unit area

Sorry I couldn't post the graph, but I interpreted it as

and got . Did I misinterpret the graph?*Last edited by Monox D. I-Fly (2018-03-19 01:35:18)*

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

hi Monox D. I-Fly

When you integrate an 'area under graph' that is negative it will come out as negative. So it's always advisable to draw the graph so you can see what's happening. There's a great function plotter here:

http://www.mathsisfun.com/data/function-grapher.php?

Here's a screen shot of the problem with some areas shaded.

It's that pink area C that is causing the difficulty.

You have calculated

I think that gives:

(A+B) - (B+C) -C = A + B - B - C - C = A - 2C which I make 58/3.

It appears that B and C have the same area (by coincidence) which complicates matters somewhat.

Does the question want A + B + (-C) or just A + B. The latter does give one of the multi choice answers.

**Another opinion here please.**

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 166
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IMHO the area required is just A. To calculate this, we need to know area C so we can subtract it from A+C.

Let’s calculate A+C. It’s

Area C is

Hence area A is

Hmm, I get a different answer myself.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

hi Alg Num Theory

Thanks for your ideas. Could be A. Or maybe the questioner meant A+C; at least that is one of the multi choice answers. Trouble is the y axis isn't a boundary in any case. ??? But A+C = A+B so you could get the 'right' answer by doing totally the wrong thing. Poor question.

Years ago I was marking for an exam board. There was an easy 'mean' of these numbers question; correct answer = 3. We were told to award the marks even without any working seen as the working could easily be done in your head. So what to do when a candidate carefully worked out the median and still got 3. Obviously they had done the wrong thing, but if they had put no working they would get the marks. Thankfully, nowadays, exam questions are subjected to much scrutiny before launching them on the candidates.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,161

The question asks for A + C.

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 166
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In that case, the *y*-axis shouldn’t come into the question: it should just be area bounded by the two curves and the line *x*=3. I agree with Bob: the question is not very well stated.

*Last edited by Alg Num Theory (2018-03-20 00:40:03)*

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,910

I concur with everyone here, using some Geogebra, we can confirm the solution is 18 u^2.

*Last edited by Mathegocart (2018-03-22 23:41:41)*

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 166
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The area between two curves is always the integral of the top curve minus the bottom curve. It doesn’t matter if part or all of this area is below the *x*-axis: as long as you take the top curve minus the bottom curve and integrate, the result is always positive.

Take these examples:

They are plotted here. Find the area bounded by them and their points of interesection. Notice that this area is wholly below the *x*-axis. However the definite integral

is positive; this is the area required.

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