Evaluate \(\int_{1}^{3}(x^2 - 1)dx\)
A
\(\frac{2}{3}\)
B
\(-\frac{2}{3}\)
C
\(-6\frac{2}{3}\)
D
\(6\frac{2}{3}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\int_{1}^{3}(x^2\) - 1)dx
= \(\left[\frac{1}{3}x^3 - x\right] ^{3}_{1}\)
= (9-3) - \(\frac{1}{3}-1)\)
= 6 - \(\left(-\frac{2}{3}\right)\)
= 6+\(\frac{2}{3}\) =6\(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #8056)