$6\displaystyle\int_0^\pi|\sin 3x+\sin 2x+\sin x|\,dx$ is equal to _____
Step-by-Step Solution
Key Concept: $\sin 3x+\sin 2x+\sin x=2\sin 2x\cos x+\sin 2x=\sin 2x(2\cos x+1)$. Zeros in $[0,\pi]$: $x=0,\pi/2,2\pi/3,\pi$. Analyse sign on each subinterval.
$6\int_0^\pi|\sin 3x+\sin 2x+\sin x|\,dx=17$.
Correct Answer: 17