Let n≥2 be a natural number and 0<θ<π/2... | Indefinite Integrals

JEE Main 2019

10-01-2019 S1

Question

Let $\mathrm{n} \geq 2$ be a nutural number and $0<\theta<\pi / 2$. Then $\int \frac{\left(\sin ^{\mathrm{n}} \theta-\sin \theta\right)^{\frac{1}{\mathrm{n}}}}{\sin ^{n+1} \theta} d \theta$ is equal to (where C is a constant of integration)

Select the correct option:

$\frac{n}{n^2-1}\left(1-\frac{1}{\sin ^{n+1} \theta}\right)^{\frac{n+1}{n}}+C$

$\frac{n}{n^2+1}\left(1-\frac{1}{\sin ^{n-1} \theta}\right)^{\frac{n+1}{n}}+C$

$\frac{n}{n^2-1}\left(1-\frac{1}{\sin ^{n-1} \theta}\right)^{\frac{n+1}{n}}+C$

$\frac{n}{n^2-1}\left(1+\frac{1}{\sin ^{n-1} \theta}\right)^{\frac{n+1}{n}}+C$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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