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Practicing Success
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$\int\limits_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is : |
0 1 $\frac{\pi}{2}$ $\frac{\pi}{4}$ |
$\frac{\pi}{4}$ |
$I=\int\limits_0^{\pi / 2} \frac{\cos ^3 x}{\sin ^3 x+\cos ^3 x} d x$ $I=\int\limits_0^{\pi / 2} \frac{\sin ^3 x}{\sin ^3 x+\cos ^3 x} d x \Rightarrow 2 I=\int\limits_0^{\pi / 2} dx \Rightarrow I=\frac{\pi}{4}$ Hence (4) is the correct answer. |
