Integration Watch

Merdan
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Ok suppose the line crosses the positive x axis at 3 if I integrated using the limits 3 to 0,
Would I find the shaded area or 2 x the shaded are i:e(shaded are + the area below given that they are equal It looks the area below is within the range of limit and surprisingly I haven't got 0 even the range of limit includes both + and - equal areas so does anyone have any advice to criticise this as to see which area I would get depending how I integrate it....
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brianeverit
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(Original post by Merdan)
Ok suppose the line crosses the positive x axis at 3 if I integrated using the limits 3 to 0,
Would I find the shaded area or 2 x the shaded are i:e(shaded are + the area below given that they are equal It looks the area below is within the range of limit and surprisingly I haven't got 0 even the range of limit includes both + and - equal areas so does anyone have any advice to criticise this as to see which area I would get depending how I integrate it....
What equation are you using for the curve, Cartesian or parametric?
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Merdan
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(Original post by brianeverit)
What equation are you using for the curve, Cartesian or parametric?
Parametric.
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ztibor
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(Original post by Merdan)
Parametric.
For the parametric equation system the limits of integral are clear,
because for another parameter of t will be x>0 and y>0 or
x>0 and y<0 smoultaneously.

So when y=f(t) and x=g(t)

\displaystyle A=\int_{t_1}^{t_2} f(t) \cdot \frac{d g(t)}{dt} \cdot dt

I think your equations may be

\displaystyle x=3\cdot \cos t
\displaystyle y=2\cdot \sin 2t

then fro the upper shaded region the integration limits are: t from \pi/2 to 0
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