Group1Project.docx - Problem Solution The problem is asking...

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Problem: Solution: The problem is asking to find the equation of the curve, C, by calculating the area of "A" and "B." To do this, we must find the area of A using vertical cross-sections, and to find area B we must use horizontal cross-sections and set them equal to each other. First, let the point P on the middle curve equal (P, 2P 2 ). "P" is set as the x coordinate indicating that any value on the curve will show that areas A and B is equal. "2P 2 " is set as the y coordinate because the point is on the curve y=2x 2 and we replaced "x" with "P" to keep the points consistent. Now, we must find the areas of section A and B. For area A , we will be integrating with respect to x, simply take the integral of 2 x 2 x 2 from 0 to P, P being any point on the line 2 x 2 (recall that at any point P, the areas of A and B are equal). Area A = 0 P 2 x 2 x 2 dx ¿ 0 P x 2 ¿ x 3 3 { P 0 Area A = P 3 3 [combine like terms] [antiderive]
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Finding the area of B will be a little trickier than with the area of A. To find area B
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  • Winter '08
  • CATHERINEL
  • Calculus, Quadratic equation, Indian mathematics

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