Question
Paragraph: Let \(f: [0, 2 ] [0,1]\) be the function defined by \(f(x)= ^2 x\) and let \(g: [0, 2 ] [0, )\) be the function defined by \(g(x)= x 2 -x^2 \). Question: The value of 2 _0^ 2 f(x) g(x) d x- _0^ 2 g(x) d x is
JEE Advanced
Mathematics
Definite Integration
2024
JEE Advanced 2024 (Paper 2)
JEE Advanced Mathematics Question (2024) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
I=2 _0^ 2 ^2 x x 2 -x^2 _ I_1 - _0^ 2 g(x) d x Let I_1= _0^ 2 ^2 x ( 4 )^2- (x- 4 )^2 (making perfect square) apply kings I_1= _0^ 2 ^2 x ( 4 )^2- ( 2 -x )^2 add both 2 I_1= _0^ 2 ( 4 )^2- (x- 4 )^2 i.e. 2 I_1= _0^ 2 g(x) Now I=2 I_1- _0^ 2 g(x)=0
Related: Mathematics — Definite Integration · All PYQ Banks