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Section 6.1 - (1 x 2 and integrate from x =-1 to x = 2 The...

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Section 6-1: Areas Between Curves Find the area A between the curves y = 1 + x 2 y = 3 + x Sketch the area and find points of intersection We sketch the area to be calculated by sketching the two curves and finding their points of intersection M and N. To find M and N, we solve: 1 + x 2 = y = 3 + x x 2 -x - 2 = 0 (x - 2)(x + 1) = 0 M: x = -1 y = 2 N: x = 2 y = 5 Method of vertical strips We divide the area A into thin vertical strips of width dx, height (3 + x)
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Unformatted text preview: - (1 + x 2 ) and integrate from x = -1 to x = 2. The area dA of a vertical strip is: dA = [(3 + x) - (1 + x 2 )]dx Method of horizontal strips We divide the area A into thin horizontal strips of height dy and consider two cases to calculate their width. Area A1: 1 < y < 2 The area dA of a horizontal strip is: Area A2: 2 < y < 5 The area dA of a horizontal strip is:...
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