Evaluate \(\int_{1}^{3}(x^2 - 1)dx\)
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Correct Answer: Option D
Explanation:
\(\int_{1}^{3}(x^2 - 1)dx = \left[\frac{1}{3}x^2 - x\right] ^{3}_{1}\\ =(9-3)-(\frac{1}{3}-1)\\ =6-\left(-\frac{2}{3}\right)\\ =6+\frac{2}{3}=6\frac{2}{3}\)
\(\int_{1}^{3}(x^2 - 1)dx = \left[\frac{1}{3}x^2 - x\right] ^{3}_{1}\\ =(9-3)-(\frac{1}{3}-1)\\ =6-\left(-\frac{2}{3}\right)\\ =6+\frac{2}{3}=6\frac{2}{3}\)