If `f(x) = a + bx + cx^(2)` where c > 0 and `b^(2) - 4ac < 0`. Then the area enclosed by the coordinate axes,the line x = 2 and the curve y = f(x) is given by

Options

A. `(1)/(3){4f(1)+f(2)}`
B. `(1)/(2){f(0)+4f(1)}`
C. `(1)/(2){f(0)+4f(1)+f(2)}`
D. `(1)/(3){f(0)+4f(1)+f(2)}`

Answer

D

Explanation

Area `=underset(0)overset(2)(int)ydx=underset(0)overset(20)(int)(a+bx+cx^(2))dx=2a +2b+(8c)/(3)`
`=(1)/(3)(6a+6b+8c)`
`=(1)/(3){f(0)+4f(1)+f(2)}`