∫¹-1 (x² - x - 1) dx = ______?
- -3/4
- -4/3
- 4/3
- None of these
Explanation
Step 1: Evaluate the integral
∫(x² - x - 1) dx = (x³ / 3) - (x² / 2) - x
Step 2: Apply the limits of integration
[(1³ / 3) - (1² / 2) - 1] - [((-1)³ / 3) - ((-1)² / 2) - (-1)]
= [(1/3) - (1/2) - 1] - [(-1/3) - (1/2) + 1]
Step 3: Simplify the expression
= (1/3) - (1/2) - 1 + (1/3) + (1/2) - 1
= (2/3) - 2
= (2/3) - (6/3)
= -4/3
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