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Chrome File Edit View History Bookmarks People Window Help AS 100% E Wed 10:21 PM Q E e O O WeBWorK MA. x GRind the volume of x Desmos Graphing c x YThe region between x GGoogle x www.stewartcalculu x C Chegg Study l Guid x C X https phoenix goucher.edu F 102315 Substitute/2/?effectiveUse micaih685&displayMode; MathJax&key; 60KWIxjYEP... E Logged in as micaih685. WeBWorK Log Out MATHEMATICAL ASS0CIATION 0F AMERICA MAIN MENU webwork man180bt-fall2015 due f 02315 substitute 2 Courses Homework Sets Due F 102315 Substitute: Problem 2 Due F 102315 Prev Up Next Substitute Problem 2 Password/Email (2 pts) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 0, y cos(8x), x ,x 0 about the axis y Grades Problems Problem 1 Preview Answers Submit Answers Problem 2 You have attempted this problem 0 times. Problem 3 You have unlimited attempts remaining. Problem 4 Problem 5 Email instructor Problem 6 Display options View equations as: Images sMath Math Jax OLa LaTeXMathML Show saved answers? Yes

Explanation / Answer

y=0,x=0,x=/16,y=cos8x about y=-2

by washer method. volume y=-2 is

Volume = 0/16 ( (cos(8x) - (-2))^2- (0 - (-2))^2 )dx

Volume = 0/16 ( (cos(8x) +2)2 -(2)2)dx

Volume = 0/16 (4 -4+(cos2(8x) +4cos(8x) ))dx

Volume = 0/16 ( cos2(8x) +4cos(8x) ))dx

Volume = 0/16 ( (1+cos(16x))/2 +4cos(8x) ))dx

Volume = 0/16 ( (1/2)+ (1/2)cos(16x) +4cos(8x) ))dx

Volume = 0|/16 ( (1/2)x +(1/2)(sin(16x))/16    +4(sin(8x))/16) +c

Volume = 0|/16 ( (1/2)x +(1/32)(sin(16x))   +(sin(8x))/4) +c

Volume = [( (1/2)(/16) +(1/32)(sin(16/16)) +(sin(8/16))/4) +c]-[((1/2)*0 +(1/32)(sin(16*0)) +(sin(8*0))/4) +c]

Volume = [((/32) +(1/32)(0) +(1)/4) ]

Volume = (+8)/32)

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