The area of the shaded region is ... sq.units.

Step-by-step solution

From the given figure, the shaded region is bounded by the curve y = x from x = 2 to x = 9 4 and by the curve y = x from x = 9 4 to x = 5 2 . The area A of the shaded region is given by the sum of two definite integrals: A = _ 2 ^ 9 4 x , dx + _ 9 4 ^ 5 2 x , dx Evaluating the first integral: _ 2 ^ 9 4 x , dx = [- x]_ 2 ^ 9 4 = - ( 9 4 ) - (- (2 )) = - 1 2 - (-1) = 1 - 1 2 Evaluating the second integral: _ 9 4 ^ 5 2 x , dx = [ x]_ 9 4 ^ 5 2 = ( 5 2 ) - ( 9 4 ) = 1 - 1 2 Adding the two areas: A = (1 - 1 2 ) + (1 - 1