Question
Let g_ i : [ 8 , 3 8 ] R , i=1,2, and f: [ 8 , 3 8 ] R be functions such that g_ 1 (x)=1, g_ 2 (x)=|4 x- | and f(x)= ^ 2 x, for all x [ 8 , 3 8 ] Define S_ i = _ 8 ^ 3 8 f(x) g_ i (x) d x, i=1,2 The value of 48 S 2 π 2 is ____.
JEE Advanced
Mathematics
Definite Integration
2021
JEE Advanced 2021 (Paper 2)
JEE Advanced Mathematics Question (2021) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
S 2 = ∫ π 8 3 π 8 sin 2 x 4 x - π d x       … … … i S 2 = ∫ π 8 3 π 8 sin 2 3 π 8 + π 8 - x 4 3 π 8 + π 8 - x - π d x S 2 = ∫ π 8 3 π 8 cos 2 x π - 4 x d x         … … … ii From (i) and (ii), we get 2 S 2 = ∫ π 8 3 π 8 4 x - π d x 2   S 2 = π 2 16 S 2 = π 2 32 ⇒ 48 S 2 π 2 = 48 32 ⇒ 48 S 2 π 2 = 3 2 = 1 . 5
Related: Mathematics — Definite Integration · All PYQ Banks