大师作文网大学微积分求下列积分
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/14 01:06:44
大学微积分求下列积分
换元去根号,因为积分上下限为-1,1,令x=sint,则新的积分上下限为-π/2,π/2
原式=∫（1+sint+sint^2)costdsint=∫cost^2dt+∫sint*cost^2dt+∫sint^2cost^2dt
=∫（2cos2t-1)dt-∫cost^2dcost+1/4∫sin2t^2dt (∫sin2t^2dt = t/2-sin4t/8+C)
=sin2t-t-1/3cost^3+t/8-sin4t/32|-π/2,π/2
=0-π/2-0+π/16-0- (0+π/2-0-π/16-0)
=-7π/8
原式=∫（1+sint+sint^2)costdsint=∫cost^2dt+∫sint*cost^2dt+∫sint^2cost^2dt
=∫（2cos2t-1)dt-∫cost^2dcost+1/4∫sin2t^2dt (∫sin2t^2dt = t/2-sin4t/8+C)
=sin2t-t-1/3cost^3+t/8-sin4t/32|-π/2,π/2
=0-π/2-0+π/16-0- (0+π/2-0-π/16-0)
=-7π/8