Integrate (int_{-1} ^{2} (2x^2 + x) mathrm {d} x)
-
A.
(4frac{1}{2}) -
B.
(3frac{1}{2}) -
C.
(7frac{1}{2}) -
D.
(5frac{1}{4})
Correct Answer: Option C
Explanation
(int_{-1} ^{2} (2x^2 + x) mathrm {d} x)
= ([frac{2x^{2 + 1}}{3} + frac{x^{1 + 1}}{2}]_{-1} ^{2})
= ([frac{2x^{3}}{3} + frac{x^{2}}{2}]_{-1} ^{2})
= ((frac{2(2)^{3}}{3} + frac{2^2}{2}) – (frac{2(-1)^{3}}{3} + frac{(-1)^{2}}{2}))
= ((frac{16}{3} + 2) – (frac{-2}{3} + frac{1}{2}))
= (frac{22}{3} – (-frac{1}{6}))
= (frac{22}{3} + frac{1}{6})
= (frac{15}{2})
= (7frac{1}{2})
There is an explanation video available below.