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Question Number 136076 by physicstutes last updated on 18/Mar/21
findtheareabetweenthecurvey=3+2x−x2,thex−axisandtheliney=3.findthevolumeofthesolidgeneratedwhenthecurveisrotatedcompletelyabouttheliney=3
Answered by mr W last updated on 18/Mar/21
AreaA=23×(4×4−2×1)=283
Commented by mr W last updated on 18/Mar/21
volumeVx2−2x−3+y=0(x2−x1)2=(x2+x1)2−4x1x2=22−4(−3+y)=4(4−y)x2−x1=24−ydV=2π(3−y)(x2−x1)dyV=∫032π(3−y)(x2−x1)dy=4π∫03(3−y)4−ydy=4π∫30(3−y)1+3−yd(3−y)=4π∫03u1+udu=4π×215[(u+1)32(3u−2)]03=4π×2×5815=464π15
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