微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. 7. -. Find h aa of h shadd gion.. d. d -. Skch h gion nclosd h givn cuvs. Dcid whh o inga wih spc o o. Daw a pical appoimaing cangl and lal is high and widh. Thn find h aa of h gion.., 先找出兩曲線交點作為積分上下限, 8,, 則 d 8 7

微積分作業解答., 先找出兩曲線交點作為積分上下限,,, 則 / d.,,, 則 d d. Skch h gion ha lis wn h cuvs cos and sin and wn. Find h aa of h cscn-shapd gion calld a lun oundd acs of cicls wih adii and s h figu. 由圖可看出, 該斜線面積對 軸對稱, 所以 則 令

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. 則 / sin / sin sin sin cos d d 且 所以 sin. Find h num such ha h lin divids h gion oundd h cuvs and ino wo gions wih qual aa. 由圖可知對稱於 軸, 故 ] [ d 且. / / d 7. Fo wha valus of m do h lin m and h cuv nclos a gion? Find h aa of h gion. 由圖可知兩曲線相交時, 交點 m 存在, m m

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. 7. -. Find h volum of h solid oaind oaing h gion oundd h givn cuvs aou h spcifid lin. Skch h gion, h solid, and a pical disk o wash.. ais h aou ;,,, /..,, 7 7 d d 7. ais h aou ;, d d

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7.., ; aou d [ ] d /. Th gion nclosd h cuvs and is oad aou h lin. Find h a / 8 cos d d a 為 cos, 對 軸旋轉所得體積 為 與 所交會的區域對 軸旋轉所得體積

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. -7. Find h volum of h dscid solid S. 7. cap of a sph wih adius and high h., 取正, 為橢圓上半部的曲線函數. a S up an ingal fo h volum of a solid ous h donu-shapd solid shown in h figu wih adii and. B inping h ingal as an aa, find h volum of h ous. a 該圓形函數為 分成左右兩邊的函數 : 左函數 L ; 右函數,

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. 7. Find h volum common o wo sphs, ach wih adius, if h cn of ach sph lis on h sufac of h oh sph. 左邊圓形函數為 而斜線部分的函數為, / / d d 其全部體積為斜線部分對 軸旋轉體積的兩倍, 即

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. 7.. L S h solid oaind oaing h gion shown in h figu aou h -ais. Eplain wh i is awkwad o us slicing o find h volum of S. Skch a pical appoimaing shll. Wha a is cicumfnc and high? Us shlls o find. 若使用圓環法 Wash, 則必須找出 的頂點, 將其分成左右兩邊的函數, 以進行體積積分, 對於該函數而言, 難以化整為好積分的函數..,,, 8

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. -. Us h mhod of clindical shlls o find h volum of h solid oaind oaing h gion oundd h givn cuvs aou h -ais. Skch h gion and a pical shll..,,, d d. 8,, 7 78 7 8 7 / 8 d d., 先找出兩函數交點,, d d d ] [ ] [ / /

-. Us h mhod of clindical shlls o find h volum gnad oaing h gion oundd h givn cuvs aou h spcifid ais. Skch h gion and a pical shll.. aou 7.,,, ; aou d d 7.,, ; aou d d -. S up, u do no valua, an ingal fo h volum of h solid oaind oaing h gion oundd h givn cuvs aou h spcifid ais.

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7.., sin / ; aou -. Each ingal psns h volum of a solid. Dsci h solid.. d d d, 即. d, 之區域對 軸旋轉所得之體積 d d, 即 i 所圍成之區域 對 軸旋轉所得之體積 ii 體積 所圍成之區域對 軸旋轉所得之 -8. Th gion oundd h givn cuvs is oad aou h spcifid ais. Find h volum of h suling solid an mhod.., ; aou ais,, d d 8., / ; aou [ ][ ] d 8

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. 7.. Us h ac gh fomula o find h gh of h cuv,. Chck ou answ noing ha h cuv is a lin sgmn and calculaing is gh h disanc fomula. L ' d d 對於線段,, 其端點為,8,,, 所以長度為 [ ] [ 8] -. Find h gh of h cuv. /., L ' d / d 8d 令 8 d 8d 8 則 8d / / 8 8 8 d., 8 L ' d d d. sc, / L ' d / sc d / sc d sc an /., L ' d d 令 an an d d sin cos 則 d d sin cos 令 u cos du sin d / / 則 d du du u u C u u sin cos u u u u u u C u cos cos C cos

微積分作業解答 Chap 7 pplicaions of Ingaion 7.-7. C C 所以 d 7.,,S up, u do no valua, an ingal fo h gh of h cuv. d d ' d d L. Skch h cuv wih quaion / / and us smm o find is gh. L d d L ' 令 d du u 則 7 7./ / / u du u d