Doesn't change the result, but why in the last steps constant in front of the integral is 9 and not 27? Where did the 9 that came from squaring the dx/dt and dy/dt go?
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Ali
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1Ok I see what you are saying, the function is $xy$. Yes it is incorrect. – Math Lover Jan 29 '21 at 14:42
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1@MathLover the part of the integrand outside the square root has a constant of 9, and the square root contributes a constant of 3, giving a total constant of 27 – Sam Freedman Jan 29 '21 at 14:42
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1@SamFreedman yes noticed the function later. I think they knew the answer was zero and so got sloppy :) – Math Lover Jan 29 '21 at 14:45
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@MathLover Yes you're right. Besides, $9 \cdot 0 = 27 \cdot 0$ so after the fact they weren't even wrong. – Sam Freedman Jan 29 '21 at 15:03
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They forgot it. The first line of step 4 should have been:
$$\text{Area} = \int_{t = 0}^{t = \pi} (3 \sin(t))(3 \cos(t)) \sqrt{(-3\sin(t))^2 + (3\cos(t))^2} $$
Sam Freedman
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