Evaluate \(\int^{1}_{-1}(2x + 1)^2 \mathrm d x\)
A
3\(\frac{2}{3}\)
B
4
C
4\(\frac{1}{3}\)
D
4\(\frac{2}{3}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\int^{1}_{-1}(2x + 1)^2 \mathrm d x\)
= \(\int^{1}_{-1}(4x^2 + 4x + 1) \mathrm d x\)
= \(\int^{1}_{-1}\)[\(\frac{4x^3}{3} + 2x^2 + x]\)
= [\(\frac{4}{3}\) + 2 + 1] - [\(\frac{-4}{3}\)+2 -1]
= \(\frac{13}{3}\) + \(\frac{1}{3}\)
= \(\frac{14}{3}\)
= \(4 \frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #31097)