99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration
Let f ( x ) = ∫ 0 x sin 100   t sin 100   t + cos 100   t   d t , then f ( 2 π ) = ?
Options
- A2 f π 2
- B4 f π 2
- Cf π 2
- Dnone of these
Correct answer
B. 4 f π 2
Step-by-step solution
f ( x ) = ∫ 0 x sin 100   t sin 100   t + cos 100   t   d t ⇒ f ( 2 π ) = ∫ 0 2 π sin 100   t sin 100   t + cos 100   t   d t = 2 ∫ 0 π sin 100   t sin 100   t + cos 100   t   d t                   ∵   ( sin   ( 2 π - t ) ) 100 ( sin   ( 2 π - t ) 100 + ( cos   ( 2 π - t ) ) 100 = sin 100 t sin 100   t + cos 100   t = 4