Question

Find the area enclosed by the curves y=\(x^2\), x=1/4, y=0 and x=1, using integration.

Answer 1

Enclosed area

\(= \int\limits ^1_ \frac14 x^2 dx\)

\( = \left[\frac{x^3}3\right]^1_\frac14\)

\( = \frac13 \left(1 -\frac1{64}\right)\)

\( = \frac {63}{64 \times 3}\)

\(= \frac{21}{64}\)