Evaluate the definite integral: integral from 0 to 2 of (3x^2 + 2x) dx.
Answer and explanation
Correct answer: A. 12
- Step 1: Find the antiderivative: F(x) = integral of (3x^2 + 2x) dx = x^3 + x^2.
- Step 2: Apply the Fundamental Theorem of Calculus: F(2) - F(0).
- Step 3: Calculate: F(2) = (2)^3 + (2)^2 = 8 + 4 = 12. F(0) = 0. Therefore, the value is 12 - 0 = 12.
Answer
12.
Why not the others: '8' evaluates only 2^3 while ignoring 2^2; '16' calculates (2+2)^2; '10' makes an arithmetic addition error.
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