Let f x be a differentiable function defined on 0 ,   2 such that f ' x = f ' 2 - x for all x ∈ 0 , 2 , f 0 = 1 and f 2 = e 2 . Then the value of ∫ 0 2 f x d x is

Question

Let f x be a differentiable function defined on 0 , &#160; 2 such that f ' x = f ' 2 - x for all x &#8712; 0 , 2 , f 0 = 1 and f 2 = e 2 . Then the value of &#8747; 0 2 f x d x is

Aicharya · Accepted Answer

f ' x = f ' 2 - x f x = - f 2 - x + c put x = 0 f 0 = - f 2 + c c = f 0 + f 2 = 1 + e 2 so, f x + f 2 - x = 1 + e 2 I = &#8747; 0 2 f x d x I = &#8747; 0 2 f 2 - x d x 2 I = &#8747; 0 2 f x + f 2 - x d x 2 I = 1 + e 2 &#8747; 0 2 d x I = 1 + e 2

Let f x be a differentiable function defined on 0 ,   2 such that f ' x = f ' 2 - x for all x…

Solution

Let f x be a differentiable function defined on 0 , &#160; 2 such that f &#39; x = f &#39; 2 - x for all x…

Solution

Let f x be a differentiable function defined on 0 , 2 such that f ' x = f ' 2 - x for all x…