The area of the region bounded by the curve y=x^3 and the line y=4 is

y → 0

y → 4

area of curve = $\int\limits_0^4y^{\frac{1}{3}}dy=\left[\frac{3y^{\frac{4}{3}}}{4}\right]_0^4$

$=3×4^{\frac{1}{3}}$ sq. units