The value of the integral... | Calculus JEE Main 2021

JEE MAIN 2021

25-02-21 S1

Question

The value of the integral $\int \frac{\sin \theta \cdot \sin 2 \theta\left(\sin ^6 \theta+\sin ^4 \theta+\sin ^2 \theta\right) \sqrt{2 \sin ^4 \theta+3 \sin ^2 \theta+6}}{1-\cos 2 \theta} d \theta$ is: (where c is a constant of integration)

Select the correct option:

$\frac{1}{18}\left[11-18 \sin ^2 \theta+9 \sin ^4 \theta-2 \sin ^6 \theta\right]^{\frac{3}{2}}+c$

$\frac{1}{18}\left[9-2 \cos ^6 \theta+3 \cos ^4 \theta-6 \cos ^2 \theta\right]^{\frac{3}{2}}+c$

$\frac{1}{18}\left[9-2 \sin ^2 \theta-3 \sin ^4 \theta-6 \cos ^2 \theta\right]^{\frac{3}{2}}+c$

$\frac{1}{18}\left[11-18 \cos ^2 \theta+9 \cos ^4 \theta-2 \cos ^6 \theta\right]^{\frac{3}{2}}+c$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Hard

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