Evaluate the definite integral: int_{1}^{3} (3x^2 - 2x + 1) dx.
Answer and explanation
Correct answer: C. 20
- Step 1: Find antiderivative: F(x) = x^3 - x^2 + x. Step 2. Evaluate at upper limit x = 3: F(3) = 3^3 - 3^2 + 3 = 27 - 9 + 3 = 21. Step 3. Evaluate at lower limit x = 1: F(1) = 1^3 - 1^2 + 1 = 1. Step 4. Subtract: F(3) - F(1) = 21 - 1 = 20. Answer: 20. Why not the others: 21 fails to subtract F(1). 18 and 24 do not fit.
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