2005
Mathematics
67ca00ce0c643c71d77dee1f
Find the area of the figure bounded by the given pair of curves y = x2 - x + 3 and y = 3
A.
17/6 units (sq)
B.
7/6 units (sq)
C.
5/6 units (sq)
D.
1/6 units (sq)
Correct Answer: 17/6 units (sq)
Explanation
Area bounded by y = x2 - x + 3 and y = 3 x2 - x + 3 = 3 x2 - x = 0 x(x -1) = 0 x= 0 and x = 1. ∫01. (x2 - x + 3)dx = [1/3x3 - 1/2x2 + 3x]10 (1/3(1)3 - 1/2(1)2 + 3(1) - (1/3(0)3 - 1/2(0)2 + 3(0)) = (1/3 - 1/2 + 3)- 0 = (2−3+18)/6 = 17/6
Area bounded by y = x2 - x + 3 and y = 3 x2 - x + 3 = 3 x2 - x = 0 x(x -1) = 0 x= 0 and x = 1. ∫01. (x2 - x + 3)dx = [1/3x3 - 1/2x2 + 3x]10 (1/3(1)3 - 1/2(1)2 + 3(1) - (1/3(0)3 - 1/2(0)2 + 3(0)) = (1/3 - 1/2 + 3)- 0 = (2−3+18)/6 = 17/6THIS WEEK's
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