The value of _0^ 2 ^ 99 x ,dx is - Vidyadip

MCQ

The value of $\int_0^{2\pi } {{{\cos }^{99}}x\,dx} $ is

A
$1$
B
$ - 1$
C
$99$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) Let $I = \int_0^{2\pi } {{{\cos }^{99}}x\,dx.} $

Then $I=2\int_{0}^{\pi }{{{\cos }^{99}}x\,dx,\,\,\,\{\because {{\cos }^{99}}(2\pi -x)={{\cos }^{99}}x\}}$

Now, $\int_{0}^{\pi }{{{\cos }^{99}}x\,dx\,=0,\,\,\{\because {{\cos }^{99}}(\pi -x)=-{{\cos }^{99}}x\}}$

$\therefore \,\,I = 2 \times 0 = 0$.

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