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

Mathematics
JAMB 2010

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\(\frac{5}{6}\)
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Correct Answer: Option 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\(\frac{2}{3}\)

There is an explanation video available below.


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Explanation Video

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