NCERT Class 12 · Ch 7 Miscellaneous Exercise · Q40
NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 40
If f(a+b−x)=f(x), choose the expression for ∫ₐᵇx f(x)dx.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: D: (a+b)/2 · ∫ₐᵇf(x)dx.
- Let I=∫ₐᵇx f(x)dx and reflect x↦a+b−x. Then I=∫ₐᵇ(a+b−x)f(x)dx.
- Add the two forms: 2I=(a+b)∫ₐᵇf(x)dx, assuming integrability.
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