Find the area of the indicated region Enclosed by y = x and y = x^4

Question

Find the area of the indicated region Enclosed by y = x and y = x^4

Answer 1

for the interval x=0 to x=1, the area is (1/2)x^2 - (1/5)x^5 = 1/2-1/5 = 0.3

the line y=x is above the curve y=x^4 from x=0 to x=1. Or, for example, x=1/3 to x=1/2 the area is (1/2)((1/3)^2 - (1/5)(1/3)^5 -[(1/2)(1/2)^2- (1/5)(1/2)^5]

for intervals from x=1 to x = b = a number larger than 1, y=x^4 is above y=x

and the area is (1/5)x^5 - (1/2)x^2 evaluated from x=1 to x=b where b>1. Or for any interval above x=1, such as from x=2 to x=5