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})
Correct Answer: Option D
Explanation
(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 + c])
= [(frac{4}{3}) + 3 + c] – [4 + (frac{1}{3}) + c]
= (frac{8}{3}) + 3 + -1 – C
= (frac{8}{3}) + 2
= (frac{14}{3})
= (4 frac{2}{3})