同济大学第六版高等数学上下册课后习题
答案5-3
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习题5?3
1? 计算下列定积分? (1)??sin(x?)dx?
2??3 解 ??sin(x?)dx??cos(x?)2???33??2??cos4?2?11?cos???0? 3322 (2)??2 解 ??2?11dx(11?5x)dx3?
1?211?2??(11?5x)(11?5x)35?2??1151? ?16?2??1?2?1010512 (3)?02sin?cos3?d??
解 ?2sin?cos3?d????2scos3?dsin?
00???14 ??cos?2??1cos4??1cos40?1?
044244 (4)?0(1?sin3?)d??
解 ?0(1?sin3?)d???0d???0sin2?dcos??? ???(cos??cos3?) (5)??2cos2udu?
6?????0??0(1?cos2?)dcos?
?13?04????
3?1?1 解 ??2cosudu???2(1?cos2u)du?u26262???261?sin2u4??26
?(?)?(sin??sin)??361??226214??3? 8 (6)?0 解 ?02?x2dx?
?令x?2sint?22?xdx?02cost?2costdt??02(1?cos2t)dt
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1 ?(t?sin2t)2?20??2?
(7)?? 解 ??228?2y2dy? 8?2ydy?2???222224?ydy2令y?2sinx2?4?2cosx?2cosxdx
?4? ?22?1124(1?cos2x)dx?2??412(x?sin2y)2?4??4?2(??2)?
(8)?1?x2x21?x2x2dx?
解 ?112?令x?sint?cost12dx?costdt???sin2t??2(sin2t?1)dt?(?cott?t)44??24?1??4?
(9)?0x2a2?x2dx? 解 ?0xa4 ?8a2a令x?asint?a4222a?xdx?0asint?acost?acostdt?422?02sin?22tdt
4a?02(1?cos4t)dt?8t??20a4?sin4t32?20a4?? ?16 (10)?133dxx21?xdx2?
? 解 ?1令x?tant2x?21?x??tan2t?sect?sec3412tdt
1 ???2dt??sint4sint3cost??34?2?23? 3 (11)??1 解 ??1 (12) ?1411xdx5?4x?
1xdx令5?4x?u111132(5?u)du??(5u?u)?38835?4x1?? 36dx1?x?
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最新同济大学第六版高等数学上下册课后习题答案5-3
