MATHEMATICS

JAMB 2005 - Question 40

Mathematics 2005 JAMB Past Questions - Question 40: Find the area of the figure bounded by the given pair of curves y=x2-x+3 and y=3

Find the area of the figure bounded by the given pair of curves y=x2-x+3 and y=3
A:
B:
C:
D:
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Correct Answer

D

Explanation

To find the area of the figure bounded by the curves y = x^2 - x + 3 and y = 3, we need to determine the points of intersection between the two curves.Setting the two equations equal to each other:x^2 - x + 3 = 3Simplifying:x^2 - x = 0Factoring out x:x(x - 1) = 0This equation is satisfied when x = 0 or x = 1.Now, we can integrate the difference between the two curves with respect to x over the interval [0, 1] to find the area:Area = ∫[0, 1] (x^2 - x + 3 - 3) dxSimplifying:Area = ∫[0, 1] (x^2 - x) dxIntegrating:Area = [x^3/3 - x^2/2] evaluated from 0 to 1Substituting the limits:Area = (1^3/3 - 1^2/2) - (0^3/3 - 0^2/2)Simplifying:Area = (1/3 - 1/2) - (0 - 0)Area = 1/6Therefore, the area of the figure bounded by the curves y = x^2 - x + 3 and y = 3 is 1/6 square units.