Find the area of the figure bounded by the given pair of curves y = x2 - x + 3 and y = 3

Assessment: JAMB UTME - Mathematics - 2005 Subject: General Mathematics

Question 1 Report

Find the area of the figure bounded by the given pair of curves y = x2 - x + 3 and y = 3
Answer Details
To find the area bounded by the given curves, we need to find the points of intersection of the two curves. Setting the equations of the curves equal to each other gives: x^2 - x + 3 = 3 Simplifying, we get: x^2 - x = 0 x(x-1) = 0 So, x = 0 or x = 1. The curves intersect at the points (0, 3) and (1, 3). The area between the curves is given by: ∫(y = x^2-x+3)dy from y=3 to y=9 = [y^2/2 - xy + 3y] from y=3 to y=9 = [(81-9)/2 - 9 + 27] - [(9-9)/2 - 0 + 9] = 17/6 units (sq) Therefore, the answer is (a) 17/6 units (sq).
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