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Find the interval in which f(x) is increasing f(x) = ∫e t (t-1)(t-2)dt Limit is from t = 0 to t = x.

Find the interval in which f(x) is increasing
f(x) = ∫et(t-1)(t-2)dt
Limit is from t = 0 to t = x.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

f(x) = \int_{0}^{x}e^{t}(t-1)(t-2)dt
Apply Newton Leibniz formula, we have
f'(x) = e^{x}(x-1)(x-2)
f(x) is increasing in the interval
f'(x) > 0
e^{x}(x-1)(x-2) > 0
exis always +ve for all x.
So we have
(x-1)(x-2) > 0
Using wavy curve method
x\in R - [1,2]

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