Integrate ∫_(-1)^2▒(2x^2+x)dx

Integrate ∫_(-1)^2▒(2x^2+x)dx
A. 41/2
B. 31/2
C. 71/2
D. 51/4

Correct Option: Answer is C

Solution:

=∫_(-1)^2▒(2x^2+x)dx
[〖2x〗^(2+1)/3+ x^(1+1)/2]²-₁ = [〖2x〗^3/3+ x^2/2]
= (〖2(2)〗^3/3+ 2^2/2) – (〖2(-1)〗^3/3+ 〖-1〗^2/2)
(22/3+ 1/6) = 15/2 = 71/2

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