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Grade: 12

                        

Let f(x)= ∫e x (x-1)(x-2) dx. Then f decreases in the interval : (A) (∞,-2) (B) (–2, –1) (C) (1, 2) (D) (2,+∞)

11 years ago

Answers : (1)

askiitian.expert- chandra sekhar
10 Points
							

Hi pallavi,

f(x)= ∫ex (x-1)(x-2) dx

f1(x)=df(x)/dx =ex (x-1)(x-2) + C

ex > 0

(x-1)(x-2) ≥0 when x≤1 and x≥2

(x-1)(x-2) < 0 when 1<x<2

therefore      ex (x-1)(x-2) < 0 when 1<x<2

f1(x) < 0 when 1<x<2

f decreases in the interval (1,2)

11 years ago
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