KCET · Maths · Definite Integration
The value of \( \int_{-\pi / 4}^{\pi / 4} \sin ^{103} x \cdot \cos ^{101} x \mathrm{~d} \mathrm{x} \) is
- A \( \left(\frac{\pi}{4}\right)^{103} \)
- B \( \left(\frac{\pi}{4}\right)^{101} \)
- C \( 12 \)
- D \( 00 \)
Answer & Solution
Correct Answer
(D) \( 00 \)
Step-by-step Solution
Detailed explanation
\( f(x) = \sin^{103}x \cdot \cos^{101}x \) \( f(-x) = \sin^{103}(-x) \cdot \cos^{101}(-x) = (-\sin x)^{103} \cdot (\cos x)^{101} = -\sin^{103}x \cdot \cos^{101}x = -f(x) \)
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