Question

定积分计算∫√(1-cos2x)dx,积分区间是0到π

Answer 1

∫√[1-cos(2x)]dx=∫√[2(sinx)^2]dx (应用倍角公式)
=√2∫sinxdx
=√2[cos(0)-cos(π)]
=√2(1+1)
=2√2.