1-1-x-2015-1-x-1-2015-1-x-1-2015-dx-

Question Number 42358 by Tawa1 last updated on 24/Aug/18

\int_{- 1}^{1} \frac{x^{2015}}{\sqrt[2015]{1 + x} + \sqrt[2015]{1 - x}} dx

Answered by tanmay.chaudhury50@gmail.com last updated on 24/Aug/18

Υ (x) = \frac{x^{2015}}{{(1 + x)}^{\frac{1}{2015}} + {(1 - x)}^{\frac{1}{2015}}}

Υ (- x) = \frac{{(- x)}^{2015}}{{(1 - x)}^{\frac{1}{2015}} + {(1 + x)}^{\frac{1}{2015}}} = - Υ (x)

s o f (x) i s o d d f u n c t i o n \dots

\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x f o r m u l a \dots

\int_{- 1}^{1} Υ (x) d x = \int_{- 1}^{1} Υ (1 - 1 - x) d x

= \int_{- 1}^{1} - Υ (x) d x

s o 2 \int_{- 1}^{1} Υ (x) d x = 0 \int_{- 1}^{1} Υ (x) d x = 0

h e n c e \int_{- 1}^{1} \frac{x^{2015}}{{(1 + x)}^{\frac{1}{2015}} + {(1 - x)}^{\frac{1}{2015}}} d x = 0

Commented by Tawa1 last updated on 24/Aug/18

God bless you sir . what is this sign (Υ) means ? ?

Commented by tanmay.chaudhury50@gmail.com last updated on 24/Aug/18

i t s a s y m b o l \dots b u t w h o r e d m a r k e d m e a n d w h y

Commented by Tawa1 last updated on 24/Aug/18

Owk . Just thinking if the symbol means something .

Maybe the person that redmark you want to like your solution

but mistakenly redmark .

God bless you sir .

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