If \int_{0}^{2 \pi} ( \sin ^4 x+\cos ^4 x) \dx=K \int_{0}^{\pi} \sin ^2 x \dx+ {\L} \int_{0}^{\frac{\pi}{2}} \cos ^2 x \dx and {\K}, {\L} \in {\N}, then the number of possible ordered pairs ( {\K}, {\L}) is [AP EAPCET 23 May 2024 S1]

Definite Integration

Section: Mathematics

Question : 22 of 54

Marks: +1, -0

2π

∫

(sin‌4x+cos4x)‌dx=K‌

∫

sin‌2x‌dx+L‌

‌

∫

cos2x‌dx and K,L∈N, then the number of possible ordered pairs (K,L) is

[AP EAPCET 23 May 2024 S1]

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