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Integrate $\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x$ ...

Integrate $\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x$

A.

$4\frac{1}{2}$

B.

$3\frac{1}{2}$

C.

$7\frac{1}{2}$

D.

$5\frac{1}{4}$

View answer & explanation

Correct answer is C

$\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x$

= $[\frac{2x^{2 + 1}}{3} + \frac{x^{1 + 1}}{2}]_{-1} ^{2}$

= $[\frac{2x^{3}}{3} + \frac{x^{2}}{2}]_{-1} ^{2}$

= $(\frac{2(2)^{3}}{3} + \frac{2^2}{2}) - (\frac{2(-1)^{3}}{3} + \frac{(-1)^{2}}{2})$

= $(\frac{16}{3} + 2) - (\frac{-2}{3} + \frac{1}{2})$

= $\frac{22}{3} - (-\frac{1}{6})$

= $\frac{22}{3} + \frac{1}{6}$

= $\frac{15}{2}$

= $7\frac{1}{2}$

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