Q88.Let f(x) and g(x) be two functions satisfying f(x2) + g(4 −x) = 4x3 and g(4 −x) + g(x) = 0, then the value of ∫4−4 f(x2)dx is
What This Question Tests
The question requires using given functional equations to deduce properties of the functions (even/odd) and then apply definite integral properties to evaluate the integral over a symmetric interval.
Concepts Tested
Formulas Used
∫(-a to a) f(x) dx = 2∫(0 to a) f(x) dx if f(x) is even
∫(-a to a) f(x) dx = 0 if f(x) is odd
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📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Properties of definite integrals
- Year
- 2021
- Shift
- 18 Mar Shift 1
- Q Number
- Q88
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
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