f-x-1-1-2-x-1-1-3-x-1-4-x-1-find-1-5-f-x-dx-5-1-f-x-dx-

Question Number 157016 by amin96 last updated on 18/Oct/21

f (x) = \frac{1}{1 + 2^{x}} + \frac{1}{1 + 3^{x}} + \frac{1}{4^{x} + 1}

f i n d \int_{1}^{5} f (x) d x + \int_{- 5}^{- 1} f (x) d x

Answered by amin96 last updated on 18/Oct/21

f (- x) = \frac{2^{x}}{1 + 2^{x}} + \frac{3^{x}}{1 + 3^{x}} + \frac{4^{x}}{1 + 4^{x}}

f (x) + f (- x) = 3

\int_{1}^{5} f (x) d x + \underset{x = - x}{\underset{⏟}{\int_{- 5}^{- 1} f (x) d x}} \Rightarrow d x = - d x x [1; 5]

\int_{1}^{5} f (x) d x - \int_{5}^{1} f (- x) d x = \int_{1}^{5} (f (x) + f (- x)) d x =

= \int_{1}^{5} 3 d x = 3 x ∣_{1}^{5} = 15 - 3 = 12

Commented by amin96 last updated on 18/Oct/21

i t s t r u e ?

Commented by puissant last updated on 18/Oct/21

G o o d s i r . .