Question

\(\int _0^π|sin2x|\,\text{d}x =\)

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(-1\)

Hint:

Split at pi/2 where sin 2x changes sign and double the first piece by symmetry.

Answer 1

The Correct Option is C

Step 1: Area view
$|\sin 2x|$ has period $\pi/2$, so $[0, \pi]$ holds two identical humps.

Step 2: One hump
$\int_0^{\pi/2}\sin 2x\,dx = 1$.

Step 3: Total
Two humps give 2. Option (C).

Final Answer:
Option (C). \[ \boxed{2} \]