Question

Sum of all the values of x in the interval [0, 314] 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$\pi$

$sinx=0$
$x=n\pi +0$, where $x\in [0,314]$
Thus, $x=0,\pi ,2\pi ,3\pi ,....100\pi$
Sum of all the values= $0+\pi +2\pi +...+100\pi$
= $\pi (1+2+3+...+100)$
= $\pi \frac{100\times 101}{2}$ Using formula of an AP, $sum=\frac{n(2a+(n-1\left)d\right)}{2}$
= $5050\pi$