Question
Let and be the real numbers such that _ x 0 1 x^3 ( 2 _0^x 1 1-t^2 d t+ x x )=2. Then the value of + is _______
JEE Advanced
Mathematics
Limits
2025
JEE Advanced 2025 (Paper 1)
JEE Advanced Mathematics Question (2025) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
_ x 0 2 _0^x 1 1-t^2 d t+ x x x^3 aligned & = _ x 0 2 ( 1 1-x^2 )+ x- x x 3 x^2 \\ & = 2 (1-x^2 )^ -1 + (1- x^2 2! + x^4 4! )- x (x- x^3 3! + x^5 5! ) 3 x^2 \\ & = 2 (1+x^2+x^4 )+ (1- x^2 2! + x^4 4! )- (x^2- x^4 3! ) 3 x^2 aligned aligned & = ( 2 + )+ x ^2 ( 2 - 2 - )+ x ^4() 3 x ^2 =2( Given ) \\ & 2 + =0 and -3 6 =2 \\ & =-2 and =12+3 \\ & =- 12 5 and = 24 5 aligned + = 12 5 =2.40
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