KCET · Maths · Definite Integration
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{1000} x d x}{\sin ^{1000} x+\cos ^{1000} x} \) is equal to
- A \( 1000 \)
- B \( \pi \)
- C \( \frac{\pi}{2} \)
- D \( \frac{\pi}{4} \)
Answer & Solution
Correct Answer
(D) \( \frac{\pi}{4} \)
Step-by-step Solution
Detailed explanation
\( I = \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{1000} x}{\sin ^{1000} x+\cos ^{1000} x} dx \) Using \( \int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) dx \):
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