Given-that-f-x-x-2x-1-1-t-4-dt-a-state-its-domain-b-is-f-x-even-or-odd-

Question Number 167520 by MikeH last updated on 18/Mar/22

Given that f (x) = \int_{x}^{2 x} \frac{1}{\sqrt{1 + t^{4}}} d t

(a) state its domain

(b) is f (x) even or odd ?

Answered by aleks041103 last updated on 18/Mar/22

(a) o b v . f (x) i s d e f i n e d f o r \forall x \in R .

(b) f (- x) = \int_{- x}^{- 2 x} \frac{d t}{\sqrt{1 + t^{4}}} =

= - \int_{- x}^{- 2 x} \frac{d (- t)}{\sqrt{1 + {(- t)}^{4}}} = - \int_{x}^{2 x} \frac{d t}{\sqrt{1 + t^{4}}} = - f (x)

\Rightarrow f (- x) = - f (x)

\Rightarrow f (x) i s o d d .