AP EAMCET202023 Sep 2020Morning ShiftPhysicsMotion in One DimensionActual
If f ' x = a sin x + b cos x , f ' 0 = 4 , f 0 = 3 and f π 2 = 5 , then f x =
Options
- A- 2 cos x - 4 sin x + 1
- B2 cos x + 4 sin x + 1
- C2 sin x - 4 cos x + 1
- D2 sin x + 4 cos x + 1
Correct answer
B. 2 cos x + 4 sin x + 1
Step-by-step solution
Given, f ' x = a sin x + b cos x             . . . i and f ' ( 0 ) = 4 ⇒ f ' 0 = a   sin 0 + b cos 0 ⇒ b = 4 Integrating both the sides of equation i with respect to x , ∫ f ' x   d x = ∫ a sin x + b cos x d x f x = - a cos x + b sin x + c f x = - a cos x + 4 sin x + c ∵   f 0 = 3 ,   f π 2 = 5 ⇒ f π 2 = - a cos π 2 + 4 sin π 2 + c = 4 + c ⇒ 5 = 4 + c ⇒ c = 1 ⇒ f 0 = - a cos 0 + 4 sin 0 + 1 =