Question:
If
int₀ᵃ f(2a-x)dx=m quadand int₀ᵃ f(x)dx=n,
then
int₀²a f(x)dx
is equal to:
If
int₀ᵃ f(2a-x)dx=m quadand int₀ᵃ f(x)dx=n,
then
int₀²a f(x)dx
is equal to:
Show Hint
Use substitution x→ a+b-x in definite integrals.
Updated On: Mar 20, 2026
- \(2m+n\)
- \(m+2n\)
- \(m-n\)
- m+n
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: int₀²a f(x)dx=int₀ᵃ f(x)dx+intₐ²af(x)dx
Step 2: Let x=2a-t in second integral intₐ²af(x)dx=int₀ᵃ f(2a-t)dt=m
Step 3: int₀²af(x)dx=n+m
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