If \(f(x)=sin 5 x + sin 3 x\) and \(g(x)=cos 6 x + sin 3 x\) , then the value of \( ∈t 0 π/2 [f(x) + f(-x)] [g(x) + g(-x)]dx\) is

\(f(x) = sin 5 x + sin 3 x\) is an odd function, so \(f(-x) = -f(x)\) and \(f(x) + f(-x) = 0\). The integrand is therefore \(0 × [g(x) + g(-x)] = 0\), and the integral is 0. Answer: (A) 0

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\(f(x)=sin 5 x + sin 3 x\) and \(f(x)=sin... - Solved | MCA Prep" /> \(f(x)=sin 5 x + sin 3 x\) and \(f(x)=sin... - Solved | MCA Prep" /> \(f(x)=sin 5 x + sin 3 x\) and

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Question 38

Mathematics Definite Integrals Hard

If \(f(x)=\sin^5 x + \sin^3 x\) and \(g(x)=\cos^6 x + \sin^3 x\), then the value of \(\displaystyle\int_0^{\pi/2} [f(x) + f(-x)] [g(x) + g(-x)]dx\) is

(A) 0

(B) > 1

(C) 0 and 1

(D) less than 0

✓ Correct Answer: Option A Verified Solution