Question

(a) use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit.

Answer 1

By definition, the area is
$A = \int _{0}^{1} x^{3} dx \\\\ = \frac{1}{4} [x^{4} }]_{0}^{1} \\\\ = \frac{1}{4}$

Answer:  $\frac{1}{4}$