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Find-the-area-of-the-region-R-bounded-by-the-curve-y-cosh-x-the-line-x-log-e-2-and-the-coordinate-axis-Find-also-the-volume-obtained-when-R-is-rotated-completely-about-the-x-axis-




Question Number 29116 by tawa tawa last updated on 04/Feb/18
Find the area of the region R bounded by the curve  y = cosh(x),  the line  x = log_e (2)  and the coordinate axis .  Find also the volume obtained when R is rotated   completely about the  x − axis.
FindtheareaoftheregionRboundedbythecurvey=cosh(x),thelinex=loge(2)andthecoordinateaxis.FindalsothevolumeobtainedwhenRisrotatedcompletelyaboutthexaxis.
Answered by ajfour last updated on 04/Feb/18
Area = ∫_0 ^(  ln 2) (((e^x +e^(−x) )/2))dx        =(1/2)(e^x −e^(−x) )∣_0 ^(ln 2)        =(1/2)(2−(1/2)) =(3/4)  Volume =π∫_0 ^(  ln 2) (((e^x +e^(−x) )/2))^2 dx      =(π/4)∫_0 ^(  ln 2) (e^(2x) +e^(−2x) +2)dx      =(π/4)[(e^(2x) /2)−(e^(−2x) /2)+2x]_0 ^(ln 2)      =(π/8)(4−(1/4)+4ln 2)    Volume = (π/(32))(15+16ln 2) .
Area=0ln2(ex+ex2)dx=12(exex)0ln2=12(212)=34Volume=π0ln2(ex+ex2)2dx=π40ln2(e2x+e2x+2)dx=π4[e2x2e2x2+2x]0ln2=π8(414+4ln2)Volume=π32(15+16ln2).
Commented by tawa tawa last updated on 04/Feb/18
God bless you sir
Godblessyousir

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