Evaluate \(\int^{2}_{0}(x^3 + x^2)\)dx.
- 4\(\frac{5}{6}\)
-
6\(\frac{2}{3}\)
- 1\(\frac{5}{6}\)
- 2\(\frac{5}{6}\)
The correct answer is: B
Explanation
\(\int^{2}_{0}(x^3 + x^2)\)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\(\frac{2}{3}\)
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