For f(x)=int_x^(x+1) sin(e^t)dt. Prove that: e^x|f(x)|<=2

Aarav Atkins 2022-10-12 Answered
For f ( x ) = x x + 1 sin ( e t ) d t
Prove that : e x | f ( x ) | 2
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Answers (1)

zupa1z
Answered 2022-10-13 Author has 20 answers
f ( x ) = x x + 1 sin ( e t ) d t e x f ( x ) = x x + 1 e x sin ( e t ) d t x x + 1 e t sin ( e t ) d t
Now substitute z = e t which gives
e x f ( x ) e x e x + 1 sin ( z ) d z = cos ( e x ) cos ( e x + 1 ) e x | f ( x ) | | cos ( e x ) | + | cos ( e x + 1 ) | 2
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