Evaluate (int_{-1}^{1} (x + 1)^{2}mathrm {d} x).
-
A.
(frac{8}{3}) -
B.
(frac{7}{3}) -
C.
(frac{5}{3}) -
D.
2
Correct Answer: Option A
Explanation
(int_{-1}^{1} (x + 1)^{2}mathrm {d} x equiv int_{-1}^{1} (x^{2} + 2x + 1)mathrm {d} x)
= (left. frac{x^{3}}{3} + x^{2} + x right |_{-1}^{1})
= ((frac{1^{3}}{3} + 1^{2} + 1) – (frac{(-1)^{3}}{3} + (-1)^{2} + (-1)) = frac{7}{3} + frac{1}{3} = frac{8}{3})