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: Option A
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
(int^{1}_{0})(x2 – x + 3)dx = [1/3x3 – 1/2x2 + 3x](^1 _0)
(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
= (frac{2-3+18}{6})
= 17/6