CUET Preparation Today
$\int\limits_{0}^{2\pi} \text{cosec}^7 x \, dx =$ |
0 1 4 $2\pi$ |
0 |
The correct answer is Option (1) → 0 We know, $\int\limits_{0}^{2a} f(x) dx = 0$, if $f(2a-x) = -f(x)$ Let $f(x) = \text{cosec}^7 x$. Now, $f(2\pi - x) = \text{cosec}^7(2\pi - x)$ $= -\text{cosec}^7 x = -f(x)$ $∴\int\limits_{0}^{2\pi} \text{cosec}^7 x \, dx = 0$ |
