To find the area under the curve y = 2x^4x from 0 to 1, we need to integrate the function with respect to x between the limits of integration 0 and 1.
∫[0,1] 2x^4x dx = [x^(2x+1)]/ln(2) |[0,1]
= (1^(2(1)+1))/ln(2) - (0^(2(0)+1))/ln(2)
= 1/ln(2) - 0
= 1.4427
Therefore, the area under the curve y = 2x^4x from 0 to 1 is approximately 1.4427 square units.