Mathematics

Find the area of the figure bounded by the given pair of curves y =…

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 = [1/3x31/2x2 + 3x](^1 _0)
(1/3(1)31/2(1)2 + 3(1) – (1/3(0)31/2(0)2 + 3(0))
= (1/31/2 + 3)- 0
= (frac{2-3+18}{6})
= 17/6