0

Guest

Courses New

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
9 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]

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More