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 Let f(x)= ∫ex (x-1)(x-2) dx. Then f decreases in the interval :

(A) (∞,-2)                                          (B) (–2, –1)
(C) (1, 2)                                          (D) (2,+∞)

7 years ago


Answers : (1)


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)

7 years ago

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