AP EAMCET · Maths · Definite Integration
\(\int_0^{2 \pi} \cos m x \cos n x d x+\int_{-\pi}^\pi \sin m x \cos n x d x=\)
- A 0 , if \(\mathrm{m}=\mathrm{n}\) and \(\mathrm{m}, n \in \mathbf{Z}\)
- B \(\pi\) if \(m=n, m, n \in \mathbf{Z}\)
- C \(\pi\) if \(\mathrm{m} \neq n, m, n \in \mathbf{Z}\)
- D \(2 \pi \forall m, n \in \mathbf{R}\)
Answer & Solution
Correct Answer
(B) \(\pi\) if \(m=n, m, n \in \mathbf{Z}\)
Step-by-step Solution
Detailed explanation
since \(f(-x)=\sin m(-x) \cos x(-x)\) \(\begin{aligned} & f(-x)=-\sin x \cos x \\ & =-f(x)\end{aligned}\) \(\therefore \mathrm{f}(\mathrm{x})\) is odd function…
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