设y=∫(0到x)(sint)^(1/2)dt(0

Question

设y=∫(0到x)(sint)^(1/2)dt(0<=x<=pai),则曲线y的长度是

Answer 1

y'=(sinx)^(1/2)
ds=[1+sinx]^(1/2)dx
s=∫(0,π)[1+sinx]^(1/2)dx=∫(0,π)[sin(x/2)+cos(x/2)]dx=2[sin(x/2)-cos(x/2)](0,π)=4