简单微积分算式,定积分|sin2x|dx在[3PI/4,0]上的值[0,3*pi/4]写反了 不好意思哦 我算也是1/2

0 < x < 3PI/4,
0 < 2x < 3PI/2
当0 < x < PI/2时,
0 < 2x < PI,|sin(2x)| = sin(2x)
当PI/2 < x < 3PI/4时,
PI < 2x < 3PI/2,|sin(2x)| = -sin(2x)
S_{0->3PI/4}|sin(2x)|dx
= S_{0->PI/2}|sin(2x)|dx + S_{PI/2->3PI/4}|sin(2x)|dx
= S_{0->PI/2}sin(2x)dx - S_{PI/2->3PI/4}sin(2x)dx
= -[cos(2x)/2]|{0->PI/2} + [cos(2x)/2]|{PI/2->3PI/4}
= [1/2] + [-cos(PI)]
= 1/2 + 1
= 3/2