Please help with 13 ed by2. Toy² incir-UDAon- x².brsdargXabout the y-axis.3-7 Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curvesto wpths of ongü3. y=x, y=0, x=1U: 1 0004. y=x², y = 0, x= 1, x = 2ME OUTbrg?5. y = e, y = 0, x=0, x=16₁ y = 4x = x², y = x7. y = x², y = 6x - 2x²- b'da1--8. Let V be the volume of the solid obtained by rotating aboutthe y-axis the region bounded by y = √x and y = x². FindV both by slicing and by cylindrical shells. In both casesdraw a diagram to explain your method.diy9-14. Use the method of cylindrical shells to find the volumeof the solid obtained by rotating the region bounded by the givencurves about the x-axis.y = 1, y = 3y = 2oran9. xy = 1, x = 0,10. y = √√x, x = 0,11. y = x³, y = 8,x=0 mir irigim SW fovtus a lo dignal sila12. x = 4y² - y³, x = 0uisge gniste ond ghinuesomna baan en oo baise qmos 8013. x = 1 + (y - 2)²,Manto's 28 qe me sdi ni,svivo a lox=4-(y-1)²omulov busx = 2a low 0814. x+y = 3,appaleibmol gogsteibadi, guDAYgans15-20 = Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curvesnoit pas nogalog & ydTEMS! 21 2253about the specified axis.15. y = x4, y = 0, x= 1; about x = 2Tac16. y = √x, y = 0, x = 1; about x = -1117. y = 4x - x², y = 3; about x = 118. y = x², y = 2 - x²; about x =19. y = x³, y = 0, x= 1; about y = 120. x = y² + 1, x = 2; about y =-2ogylogsontalm24. y = x, y = 2x/(1+x³)25. x = √sin y, 0≤ y ≤726. x² - y² = 7, x = 4;SECTION 7.3 VOLUME27. Use the Midpoint Ruleobtained by rotating ab= tan x, 0≤xcurve y28. (a) If the region showny-axis to form a scto estimate the vol(b) Estimate the volurx-axis.(320170y429-32Describe the solid.2JO029. 2mx³ dx2Each integral real31.27(3-y)(1-TT/432. 27 (π-x)(co-site33-38 The region beabout the specified axi:by any method.33. y = -x² + 6x -34. y = -x² + 6x -35. y² - x² = 1, y =36. y² - x² = 1, y =37₁ x² + (x - 1)² = 11:08 AM Tue Sep 20TAY ↑#13 x=1+(y-2)2 x=2y =ox=8V =so●●●b2π x [ f(x)] dx(x-3)(x-1)X=Y₂₁²²-4y+3·yə2x= 3 x=13v=√₁²2==y [1 + {y_25]уV=(y-2)il 56%b+за4x=22 y=1(y-2)(y-2)y²-4y+2

Question

Please help with 13 ed by2. Toy² incir-UDAon- x².brsdargXabout the y-axis.3-7 Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curvesto wpths of ongü3. y=x, y=0, x=1U: 1 0004. y=x², y = 0, x= 1, x = 2ME OUTbrg?5. y = e, y = 0, x=0, x=16₁ y = 4x = x², y = x7. y = x², y = 6x - 2x²- b'da1--8. Let V be the volume of the solid obtained by rotating aboutthe y-axis the region bounded by y = √x and y = x². FindV both by slicing and by cylindrical shells. In both casesdraw a diagram to explain your method.diy9-14. Use the method of cylindrical shells to find the volumeof the solid obtained by rotating the region bounded by the givencurves about the x-axis.y = 1, y = 3y = 2oran9. xy = 1, x = 0,10. y = √√x, x = 0,11. y = x³, y = 8,x=0 mir irigim SW fovtus a lo dignal sila12. x = 4y² - y³, x = 0uisge gniste ond ghinuesomna baan en oo baise qmos 8013. x = 1 + (y - 2)²,Manto's 28 qe me sdi ni,svivo a lox=4-(y-1)²omulov busx = 2a low 0814. x+y = 3,appaleibmol gogsteibadi, guDAYgans15-20 = Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curvesnoit pas nogalog & ydTEMS! 21 2253about the specified axis.15. y = x4, y = 0, x= 1; about x = 2Tac16. y = √x, y = 0, x = 1; about x = -1117. y = 4x - x², y = 3; about x = 118. y = x², y = 2 - x²; about x =19. y = x³, y = 0, x= 1; about y = 120. x = y² + 1, x = 2; about y =-2ogylogsontalm24. y = x, y = 2x/(1+x³)25. x = √sin y, 0≤ y ≤726. x² - y² = 7, x = 4;SECTION 7.3 VOLUME27. Use the Midpoint Ruleobtained by rotating ab= tan x, 0≤xcurve y28. (a) If the region showny-axis to form a scto estimate the vol(b) Estimate the volurx-axis.(320170y429-32Describe the solid.2JO029. 2mx³ dx2Each integral real31.27(3-y)(1-TT/432. 27 (π-x)(co-site33-38 The region beabout the specified axi:by any method.33. y = -x² + 6x -34. y = -x² + 6x -35. y² - x² = 1, y =36. y² - x² = 1, y =37₁ x² + (x - 1)² = 11:08 AM Tue Sep 20<5→>TAY ↑#13 x=1+(y-2)2 x=2y =ox=8V =so●●●b2π x [ f(x)] dx(x-3)(x-1)X=Y₂₁²²-4y+3·yə2x= 3 x=13v=√₁²2==y [1 + {y_25]уV=(y-2)il 56%b+за4x=22 y=1(y-2)(y-2)y²-4y+2>>

Accepted Answer

v=2π∫13y(1+(y-2)2dy v=2π∫13y(1+y2-4y+4)dyv=2π∫13(y+y3-4y2+4y)dy

v = fb an V (x − 3)(x x= y₁²³-4y+3 чуте x = 3 X b 2₁₁ × [ f(x)] dx 29 x= 1x 2 y