Let the area of the region bounded by the curve y= x, x , lines x=0, x= 3 2 , and the x -axis be A. Then, A + A ² is equal to _ _ _ _ .

Step-by-step solution

A = ₀^ /4 x , dx + _ /4 ^ x , dx + _ ^ 5 /4 - x , dx + _ 5 /4 ^ 3 /2 - x , dx A = ( x)₀^ /4 + (- x)_ /4 ^ + ( x)_ ^ 5 /4 + ( x)_ 5 /4 ^ 3 /2 A = 1 2 + 1 2 + 1 + 1 - 1 2 + 1 - 1 2 = 3 A^2 + A = 12