If the area of the region bounded by y= x , y= x, x= 4 and x= is bisected by the line x=a , then (a+ 4 )=

Step-by-step solution

According to the question, _ 4 ^a( x- x) d x= _a^ ( x- x) d x aligned [- x- x]_ 4 ^a & =[- x- x]_a^ - a & - a+ 1 2 + 1 2 =1+ a+ a 2 -1 & =2( a+ a) 2 -1 2 & = a+ a 2 -1 2 2 & = 1 2 a+ 1 2 a 2 -1 2 2 & = a 4 + a 4 2 -1 2 2 & = (a+ 4 ) aligned