What is the area of the region bounded by x-asix, the curve y=f(x) and the two ordinates `x=1andx=(3)/(2)`?

Options

A. `(5)/(12)` square unit
B. `(7)/(12)` square unit
C. `(2)/(3)` square unit
D. `(11)/(12)`square unit

Answer

D

Explanation

Area required for given region is
`A_(2)=underset(1)overset(3//2)intf(x)dx`
`=underset(1)overset(3//2)int[x^(2)+x-1]dx`
`=[(1)/(3)x^(3)+(1)/(2)x^(2)-x]_(1)^(3//2)`
`A_(2)=((1)/(3)((27)/(8)+(1)/(2)((9)/(4))-(3)/(2))-((1)/(3)(1)+(1)/(2)(1)-1)`
`A_(2)= (11)/(12)` square unit