Let f : R → R be a function such that f 2 - x = f 2 + x and f 4 - x = f 4 + x , for all x ∈ R and ∫ 0 2 f x d x = 5 . Then the value of ∫ 10 50 f x d x is

Question

Let f : R &#8594; R be a function such that f 2 - x = f 2 + x and f 4 - x = f 4 + x , for all x &#8712; R and &#8747; 0 2 f x d x = 5 . Then the value of &#8747; 10 50 f x d x is

Aicharya · Accepted Answer

f 2 - x = f 2 + x and f 4 - x = f ( 4 + x ) Then curve is symmetric about x = 2 and x = 4 &#8756; &#160; &#160; &#160; The curve is periodic with period 4 Given &#8747; 0 2 f x d x = 5 &#8747; 0 4 f x d x = 2 &#8747; 0 2 f x d x = 10 &#8747; 10 50 f x d x = &#8747; 2 4 + 2 12 4 + 2 f x d x = 12 - 2 &#8747; 0 4 f x d x = 10 &#215; 10 = 100

Let f : R → R be a function such that f 2 - x = f 2 + x and f 4 - x = f 4 + x , for all x ∈ R…

Solution

Let f : R &#8594; R be a function such that f 2 - x = f 2 + x and f 4 - x = f 4 + x , for all x &#8712; R…

Solution

Let f : R → R be a function such that f 2 - x = f 2 + x and f 4 - x = f 4 + x , for all x ∈ R…