Evaluate (int_{-2}^{3} (3x^{2} – 2x – 12) mathrm {d} x)
-
A.
-30 -
B.
-18 -
C.
-6 -
D.
6
Correct Answer: Option A
Explanation
(int (3x^{2} – 2x – 12) mathrm {d} x = frac{3x^{2 + 1}}{2 + 1} – frac{2x^{1 + 1}}{2} – 12x)
= (x^{3} – x^{2} – 12x)
((x^{3} – x^{2} – 12x)|_{-2}^{3} = ((3^{3}) – (3^{2}) – 12(3)) – ((-2^{3}) – (-2^{2}) – 12(-2)))
= ((27 – 9 – 36) – (-8 – 4 + 24) = -18 – 12 = -30)