MATHEMATICS

JAMB 2012 - Question 39

Mathematics 2012 JAMB Past Questions - Question 39: Evaluate integral 2,1 ( x² - 4x) dx

Evaluate integral 2,1 ( x² - 4x) dx
A:
B:
C:
D:
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Correct Answer

D

Explanation

To evaluate the integral ∫[2,1] (x² - 4x) dx, we can use the power rule for integration.First, let's integrate x²:∫ x² dx = (1/3) x³ + CNext, let's integrate -4x:∫ -4x dx = -2x² + CNow, let's evaluate the definite integral from 2 to 1:∫[2,1] (x² - 4x) dx = [(1/3) x³ - 2x²] evaluated from 2 to 1                    = [(1/3) (1)³ - 2(1)²] - [(1/3) (2)³ - 2(2)²]                    = [(1/3) - 2] - [(8/3) - 8]                    = (1/3 - 2) - (8/3 - 8)                    = (-5/3) - (-16/3)                    = -5/3 + 16/3                    = 11/3Therefore, the value of the integral ∫[2,1] (x² - 4x) dx is 11/3.