clintmyster
Prophet 9 FTW
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Integration Question (proof) (1 Viewer)
- Thread starter clintmyster
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clintmyster
Prophet 9 FTW
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- Nov 12, 2007
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- 2009
- Uni Grad
- 2015
anyone?
lyounamu
Reborn
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1. Area bounded = bh + unknown area (where base = x and h = deltay)
i.e. = x . deltay + unknown area that is approximately half the size of deltax . delta y
A1 = x . deltay < x . deltay + unknown area
And A2 = (x+deltax) . deltay = x . delta y + delta x . delta y > x . deltay + unknown area
Therefore, A1 < Area bounded < A2
Whether you get a mark for this question or not will really depend on your ABILITY TO explain your way through. I will strongly recommend you to try to come up with cohesive response that follows the detailed process of working out that answers the QUESTION.
2. As deltay becomes 0, the shaded strip's area approaches 0 as well. Therefore, the area bounded by the curve, y-axis and y=c and y=d can be found by calculating the area under the curve. Since it's on the y=axis, the formula is rather I(x . dy) rather than I(y . dx). And the terminals are c and d, so the I= c->d (x. dy) represents the area under the curve on y-axis which is also bounded by y=c and y=d.
3. You can do the hence part. It's pretty easy.
i.e. = x . deltay + unknown area that is approximately half the size of deltax . delta y
A1 = x . deltay < x . deltay + unknown area
And A2 = (x+deltax) . deltay = x . delta y + delta x . delta y > x . deltay + unknown area
Therefore, A1 < Area bounded < A2
Whether you get a mark for this question or not will really depend on your ABILITY TO explain your way through. I will strongly recommend you to try to come up with cohesive response that follows the detailed process of working out that answers the QUESTION.
2. As deltay becomes 0, the shaded strip's area approaches 0 as well. Therefore, the area bounded by the curve, y-axis and y=c and y=d can be found by calculating the area under the curve. Since it's on the y=axis, the formula is rather I(x . dy) rather than I(y . dx). And the terminals are c and d, so the I= c->d (x. dy) represents the area under the curve on y-axis which is also bounded by y=c and y=d.
3. You can do the hence part. It's pretty easy.
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