Area included between curves `y=x^(2)-3x+2 and y=-x^(2)+3x-2` is

Options

A. `1/6` sq unit
B. `1/2` sq unit
C. sq unit
D. `1/3` sq unit

Answer

D

Explanation

Required area
` = 2 int _ 1 ^ 2 ( - x ^ 2 + 3x - 2 ) dx `
` (because ` both portions are of same area )
` = 2 [ - ( x ^ 3 ) /( 3 ) + ( 3x^ 2 ) /( 2 ) - 2x ] _ 1 ^ 2 `
` = 2 [ - ( 8 ) /( 3) + 6 - 4 - ( - ( 1 ) /( 3 ) + ( 3 ) /( 2 ) - 2 ) ] `
` = 2[ - ( 8 ) /( 3 ) + 2 + ( 5) / ( 6 ) ] = ( 1 ) / ( 3 ) ` sq unit.