Question

integration of mod sinx from pi to 10pi​

Answer 1

Answer

Note that sin is negative on [,2]∪[3,4]∪⋯∪[9,10] and positive otherwise. So

∫100|sin|d=5∫0sin−5∫2sind

by periodicity. But this is 5⋅2−5⋅(−2)=20.