JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f\) and \(g\) be continuous functions on \([0, a]\) such that \(f(x) = f(a -x)\) and \(g(x) + g(a -x) = 4\), then \(\int\limits_0^a {f\left( x \right)g\left( x \right)dx} \) is equal to
- A \(4\int\limits_0^a {f\left( x \right)dx} \)
- B \(\int\limits_0^a {f\left( x \right)dx} \)
- C \(2\int\limits_0^a {f\left( x \right)dx} \)
- D \(-3\int\limits_0^a {f\left( x \right)dx} \)
Answer & Solution
Correct Answer
(C) \(2\int\limits_0^a {f\left( x \right)dx} \)
Step-by-step Solution
Detailed explanation
\({\mathrm{I}=\int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{g}(\mathrm{x}) \mathrm{d} \mathrm{x}=\int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{g}(\mathrm{a}-\mathrm{x}) \mathrm{d} \mathrm{x}} \)…
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