The area (in sq units) bounded by the curves y^2=4 x and x^2=4 y is

Step-by-step solution

Given curves are y^2=4 x and x^2=4 y . The intersection point is x^4=16 y^2=16(4 x) array rlrl & x (x^3-64 ) & =0 & & x & =0,4 & & y & =0,4 array Hence, intersection point is O(0,0) and A(4,4) Required area = shaded region of the curve aligned & = (y₂-y₁ ) d x & = ₀^4 ( 4 x - x^2 4 ) d x & = [ 2 x^ 3 / 2 3 / 2 - x^3 12 ]₀^4 & = [ 4 3 (4)^ 3 / 2 - (4)^3 12 -(0-0) ] & = ( 32 3 - 64 12 )= 128-64 12 & = 64 12 = 16 3 sq units aligned