第十章定积分的应用 即面积函数为A(y)=x2-2x2 arcsin,故 V=|(3-2 S3平面曲线的弧长与曲率 1.求下列曲线的弧长 ≤x≤ (3)x=a∞s3t,y=asin3t(a>0),0≤t≤2r; (4)I= a(oost tsint),y= a(sint-toost(a >0),0<ts 2 (5)r=asin3(a>0),0≤0≤3x; (6)r=a0(a>0),0≤0≤2x 解(1)由于y=3x,故 dr (1 (10√10-1) (2)由√x+ 1得y=(1 )2,0≤x≤1, 从而,y=-(1-√x)/x,所以, 2x-2√x+1d√x =1+y2ln(1+√2) (3)由于x′=-3aos2tint,y=3ain2tost,所以 S 3avsin2toos't (sin?t +cost )dt sin2t i dt 6 (4)因为x= atcost,y= atsina,所以