Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

Step-by-step solution

Given k = ₀^ /4 x , dx k = [- x]₀^ /4 = - ( 4 ) + (0) = 1 - 1 2 The required area is A = _ /4 ^ /2 x , dx A = [- x]_ /4 ^ /2 = - ( 2 ) + ( 4 ) = 1 2 From the expression for k , we have 1 2 = 1 - k Therefore, A = 1 - k Answer: 1-k