Evaluate (int_{0}^{2} (8x – 4x^{2}) mathrm {d} x).
-
A.
(-16) -
B.
(frac{-16}{3}) -
C.
(frac{16}{3}) -
D.
(16)
Correct Answer: Option C
Explanation
(int_{0}^{2} (8x – 4x^{2}) mathrm {d} x = (frac{8x^{1 + 1}}{2} – frac{4x^{2+1}}{3})|_{0}^{2})
= ((4x^{2} – frac{4x^{3}}{3}) |_{0}^{2})
= ((4(2^2) – frac{4(2^3)}{3}))
= (16 – frac{32}{3} = frac{16}{3})