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Not all equations qualify as functions. |
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| To be a function an equation must pass the vertical line test. | |||
| That is, if you can draw a vertical line | |||
| through more than one point on the graph of an equation. | |||
| It is not a function. | |||
| OK, but even if an equation is NOT a function, | |||
| can we find an integral and calculate an area between the function and an axis? | |||
| Do you think, for example, we could find the area between the equation: | |||
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X = Y2 - 1 |
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| and the Y axis, from Y = -1 to Y = 1? | |||
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| WELL SURE! | |||
| We're hot shot calculus types now, | |||
| we can do ANYTHING! | |||
| (well almost anything) | |||
| We work this problem just like we would work the Y = X2-1 problem, | |||
| ONLY SIDEWAYS! | |||
| Since the whole area we want is where X is negative, | |||
| it's like the ones we did before where Y was negative. | |||
| We have to subtract the value where the area is on the negative side of the axis, | |||
| to get a positive answer. | |||
| So we have: | |||
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| In this problem Y is the independent variable, so dY = 1. | |||
| Since dY = 1, we were allowed to tack it on anywhere we needed it | |||
| Finding the integral and solving, we get: | |||
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copyright 2005 Bruce Kirkpatrick |
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