Answer
$$A = \frac{3}{{10}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = x,{\text{ }}g\left( x \right) = {x^4} \cr
& {\text{From the graph shown below}} \cr
& f\left( x \right) \geqslant g\left( x \right){\text{ on the interval }}0 \leqslant x \leqslant 1 \cr
& {\text{The area is given by}} \cr
& A = \int_0^1 {\left( {x - {x^4}} \right)} dx \cr
& {\text{ Integrate}} \cr
& A = \left[ {\frac{1}{2}{x^2} - \frac{1}{5}{x^5}} \right]_0^1 \cr
& A = \left[ {\frac{1}{2}{{\left( 1 \right)}^2} - \frac{1}{5}{{\left( 1 \right)}^5}} \right] - \left[ {\frac{1}{2}{{\left( 0 \right)}^2} - \frac{1}{5}{{\left( 0 \right)}^5}} \right] \cr
& {\text{Simplifying}} \cr
& A = \frac{1}{2} - \frac{1}{5} \cr
& A = \frac{3}{{10}} \cr} $$
