Question

Sum of all the values of $x$ in the interval $[0,100\pi ]$ satisfying the equation $\sin x=0$ is

• A. $4950\pi$
• B. $5050\pi$
• C. $5151\pi$
• D. none of these

Answer 1

The correct option is B $5050\pi$

$\sin x=0\Rightarrow x=0,\pi ,2\pi ,3\pi ..............100\pi$

Now, $Sum=0+\pi +2\pi +3\pi +..................100\pi =\pi (\frac{100\ast (100+1)}{2})=5050\pi$

Therefore, Answer is $5050\pi$