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JAMB Mathematics 2010 Paper

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Question : 44

Total: 49

Evaluate

\int\limits_{0}^{2}(x^3 + x^2)

dx.

4 $\frac{5}{6}$
6 $\frac{2}{3}$
1 $\frac{5}{6}$
2 $\frac{5}{6}$

Solution:

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

= (

\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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