f-x-is-a-continuous-function-forall-real-values-of-x-and-satisfies-0-x-f-t-dt-x-1-t-2-f-t-dt-x-16-8-x-6-3-A-Find-A-

Question Number 94135 by redmiiuser last updated on 17/May/20

f (x) i s a c o n t i n u o u s f u n c t i o n f o r a l l r e a l v a l u e s o f x a n d s a t i s f i e s \int_{0}^{x} f (t) . d t = \int_{x}^{1} t^{2} . f (t) . d t + \frac{x^{16}}{8} + \frac{x^{6}}{3} + A

F i n d A ?

Commented by john santu last updated on 17/May/20

f (x) = - x^{2} f (x) + {2 x}^{15} + {2 x}^{5}

f (x) = \frac{{2 x}^{15} + {2 x}^{5}}{1 + x^{2}} = \frac{2 {(x^{2})}^{7} x + 2 {(x^{2})}^{2} x}{x^{2} + 1}

= g (x) - \frac{4 x}{x^{2} + 1}

A = - 4

Commented by redmiiuser last updated on 19/May/20

n o .

W r o n g A n s w e r ? ?