Question

The value of $\int _ { 0 } ^ { 2 \pi } \cos ^ { 99 } x d x$ is

• A. 1
• B. $- 1$
• C. 99
• D. 0

Answer 1

Answer: (D)

0

Answer 2

Let $I = \int _ { 0 } ^ { 2 \pi } \cos ^ { 99 } x d x$

Then

Now, $\int _ { 0 } ^ { \pi } \cos ^ { 99 } x d x = 0 , \left\{ \because \cos ^ { 99 } ( \pi - x ) = - \cos ^ { 99 } x \right\}$

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