Let f : R → R be a continuous function. Then lim x → π / 4 π 4 ∫ 2 sec 2 x f ( x ) d x x 2 - π 2 16 is equal to:

Step-by-step solution

  lim x → π 4 π 4 ∫ 2 s e c 2 x f x d x x 2 - π 2 16 Using L-Hospital's rule, we get = lim x → π 4 π 4 f sec 2 x · 2 · sec x · sec x · tan x - 0 2 x = π 4 · 2 ( 2 ) 2 · ( 1 ) · f ( 2 ) 2 · π 4 = 2 f 2