Let f: R → R such that f(x + 2y) = f(x) + f(2y) + 4xy, ∀ x, y ϵ R

1.	Let f: R → R such that f(x + 2y) = f(x) + f(2y) + 4xy, ∀ x, y ϵ R and f(0) = 0. If I1=∫10f(dx),I2=∫0−1f(x)dx,and I3=∫1−1f(x)dx,then
Answer» Let f: R $\to$ R such that f(x + 2y) = f(x) + f(2y) + 4xy, $\forall$ x, y $ϵ$ R and f(0) = 0. If $I_{1} = \int_{0}^{1} f (d x), I_{2} = \int_{- 1}^{0} f (x) d x, a n d I_{3} = \int_{- 1}^{1} f (x) d x, t h e n$

Let f: R → R such that f(x + 2y) = f(x) + f(2y) + 4xy, ∀ x, y ϵ R and f(0) = 0. If I1=∫10f(dx),I2=∫0−1f(x)dx,and I3=∫1−1f(x)dx,then

Answer»

Let f: R $\to$ R such that f(x + 2y) = f(x) + f(2y) + 4xy, $\forall$ x, y $ϵ$ R and f(0) = 0.

If $I_{1} = \int_{0}^{1} f (d x), I_{2} = \int_{- 1}^{0} f (x) d x, a n d I_{3} = \int_{- 1}^{1} f (x) d x, t h e n$