Evaluate \(\int^{2}_{0}(x^3 + x^2)\)dx.

A.

4\(\frac{5}{6}\)

B.

6\(\frac{2}{3}\)

C.

1\(\frac{5}{6}\)

D.

2\(\frac{5}{6}\)

Correct answer is B

\(\int^{2}_{0}(x^3 + x^2)\)dx = \(\int^{2}_{0}\)(\(\frac{x^4}{4} + {\frac {x^3}{3}}\))

= (\(\frac{2^4}{4} + {\frac {2^3}{3}}\)) - (\(\frac{0^4}{4} + {\frac {0^3}{3}}\))

= (\(\frac{16}{4} + {\frac {8}{3}}\)) - 0

= \(\frac{80}{12}

= {\frac {20}{3}}\) or 6\(\frac{2}{3}\)