If n \geq 2 is a natural number and 0< \theta< \frac{\pi}{2}, then \int { (\cos ^n \theta-\cos \theta) ^{1 \/ n}}/{\cos ^{n+1} \theta} \sin \theta d \theta= [AP EAPCET 21 May 2024 Shift 1]

Correct Answer is : nn−1(cos(1−n)θ−1)2+c

\frac{n}{n-1} (\cos ^{(1-n)} \theta-1) ^2+c

\frac{n}{(n+1)(1-n)} (\cos ^{(1-n)} \theta-1) ^{1+\frac{1}{n}}+c

\frac{1}{n-1} (\cos ^{(n-1)} \theta-1) ^2+c

\frac{n}{1-n^2} (1-\cos ^{(1-n)} \theta) ^{(n+1) \/ n}

Indefinite Integration

Section: Mathematics

Question : 66 of 89

Marks: +1, -0

If n≥2 is a natural number and 0<θ<‌

, then
∫‌

(cosnθ−cos‌θ)1∕n

cosn+1θ

sin‌θdθ=

[AP EAPCET 21 May 2024 Shift 1]

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