The area of the region bounded by the curve y = 2^ kx and x = 0, x = 2 , in first quadrant is 2 2 , then the value of k is

Step-by-step solution

The area of the region is given by A = ₀² 2^ kx dx A = [ 2^ kx k 2 ]₀² A = 2^ 2k - 1 k 2 Given that the area is 2 2 : 2^ 2k - 1 k 2 = 2 2 2^ 2k - 1 = 2k Checking the given options, for k = 1 2 : 2^ 2(1/2) - 1 = 2 ( 1 2 ) 2 - 1 = 1 This satisfies the equation, hence k = 1 2 . Answer: 1 2