Class 12 Integrals · Mcq Single Correct1 Marksintegration
Class 12 Maths · Integrals · Mcq Single Correct #15
Let a>0 and f,g be continuous on [0,a], with f(x)=f(a-x) and g(x)+g(a-x)=a. Find \(I=\int_0^a f(x)g(x)dx\).
✅ Step-by-Step Solution
Final Answer: Option (B): \(\frac a2\int_0^a f(x)dx\)
- Reflection gives I=∫₀ᵃ f(x)[a−g(x)]dx=a∫₀ᵃf(x)dx−I. Therefore 2I=a∫₀ᵃf(x)dx.
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