The value of the integral I = ∫ 0 π 2 sin 3 ⁡ x - cos 3 ⁡ x 1 + sin 6 ⁡ x cos 6 ⁡ x d x is equal to

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The value of the integral

I = \int_{0}^{\frac{π}{2}} \frac{\sin^{3} x - \cos^{3} x}{1 + \sin^{6} x \cos^{6} x} d x

is equal to

MathematicsDefinite IntegrationJEE Main

Solution:

1813 Upvotes Verified Answer

The correct answer is: 0

Applying

(a + b - x)

property,

I = \int_{0}^{\frac{π}{2}} \frac{\cos^{3} x - \sin^{3} x}{1 + \cos^{6} x \sin^{6} x}

\Rightarrow I = - I \Rightarrow 2 I = 0

\Rightarrow I = 0

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