I know this is alot but I am behind I will greatly appreciate the help. Please show all your work and be neat as possible please.
Example 4 The region 9 enclosed by the curves y = 2x and y = x is rotated about the x-axis. Find the volume of the resulting solid. Solution The curves y = 2x and y = x2 intersect at the points (0, ) and (2, . The region between them, the solid of rotation, and a cross section perpendicular to the x-axis are shown in the figures below. y = 2x y =x Graph Graph Description A(X ) A cross-section in the plane Px has the shape of a washer (an annular ring) with inner radius and an outer radius so we find the cross-sectional area by subtracting the area of the inner circle from the area of the outer circle. A(x) = 4xx2 - *(x2)2 = x Therefore, we have V = 10 "A( x ) ax = 60 * ( 4x 2 - * " ) dx Need Help? Read It2. [-/1 Points] DETAILS SCALCET9 6.2.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis V = Sketch the region. 3 w 2 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help . NW -5 -4 -3 -2 -1- 2 3 4 5 -3 --4 - 5 O Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help 5 -4 5 5 - -5 -4 -3 -2 -1 N -5 -4 -3 -2 -1 -7 2 -5 -4 -3 -2 -1 3 5 Need Help? Read It Submit Answer Viewing Saved Work Revert to Last Response3. [-/1 Points] DETAILS SCALCET9 6.2.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = Vx - 1, y = 0, x = 4; about the x-axis Sketch the region. w N Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help 10 - -10 10 --5 -10 O C O Interactive 3D Graph Help Interactive 3D Graph Help .on Interactive 3D Graph Help 10- 10- 10- -10 -5 5 10 -10 10 - -5 - -5 --10 -10 --10 Need Help? Read It Watch It4. [-/1 Points] DETAILS SCALCET9 6.2.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 2v 7y, x = 0, y = 3; about the y-axis Sketch the region. 3.0 + 8 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.5 2.0 2.5 3.0 8 Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help y -15 -10 -5 -1 5 10 O O O Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help 15 15- 10 10- 6 - -5 -4 -3 -2 -1 5 -15 -10 -5 --1 5 10 15 -2 -5 -4 -3 -2 -1 1 -5 2 3 45 - -3 -10 --10 + 7-15 r- 5 T-15 Need Help? Read it Watch It5. [-/1 Points] DETAILS SCALCET9 6.2.019.MI. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = x, y = vx; about the x-axis Sketch the region. y y y 1.5 1.5 1.5/ 1.5 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 L X -X L X -03 0.5 1.0 1.5 0.5 1.0 1.5 0.5 1.0 1.5 -0.5 0.5 1.0 1.5 O -0.5 DO -0.5 -0.5 -0.5 Sketch the solid, and a typical disk or washer. Graph Graph Description Graph Graph Description Graph Graph Description Graph Graph Description 2 2 2 -2 N -2 -2 -1 2 -2 --2 .-26. [-/1 Points] DETAILS SCALCET9 6.2.021. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y; about y = 1 V = Sketch the region. - 24 Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help -2 O C Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help -2 -2 -2 Need Help? Read It7. [-/0.33 Points] DETAILS SCALCET9 6.2.017. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y = 4x; about the y-axis V = Sketch the region. y 16 X 2 4 6 8 10 12 14 16 14 2 12 3 -1 10 -2 -11 -3 2 -13 - 15 2 6 8 12 14 16 Sketch the solid and a typical disk or washer. Graph Graph Description Graph Graph Description Graph Graph Description Graph Graph Description 15 15 w 10 N -15 -10 -5 -15 10 15 -15 -10 10 15 -3 -2 -1 - -5 2 + - 1 - 3 -10 O O O Need Help? Read it Watch It8. [-/1 Points] DETAILS SCALCET9 6.2.025. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. ( = 8x , y = 0, x = 1; about x = 2 V = Sketch the region. 6 -0.5 0.5 1.0 1.5 2.0 2.5 -0.5 0.5 1.0 1.5 2.0 -0.5 0.5 1.5 2,0 2.5 -0.5 0.5 1.0 1.5 2.0 2.5 Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help y 0-4 5 - -5 -4 -3 -2 -1 1 2 3 4 - -5 T-10 O O O Interactive 3D Graph Help Interactive 3D Graph Help teractive 3D Graph Help y y 10- - 0 10- 5 +HHHH+ -5 -4 -3 -2 -1 1 3 4 5 -5 -4 -3 -2 -1 1 2 3 45 -5 -4 -3 -2 -1 1 2 3 4 - -5 - -5 - -5 -7-10 -7-10 -10 Need Help? Read It9. [-/1 Points] DETAILS SCALCET9 6.2.023. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3 + sec(x), y = 5, _. sxs "; about y = 3 Sketch the region. --5-- -1.0 -0.5 0.5 1.0 10 .0. 0.5 1.0 O Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help -2 -1 N O Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help y 10 - 10- 5- -2 -1 -2 -2 2 -5 -10 -10 Need Help? Read It Watch It10. [-/1 Points] DETAILS SCALCET9 6.2.024. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 2 sin(x), y = 2 cos(x), 0 s x_; about y = -1 Sketch the region. -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 - - - -- Sketch the solid and a typical disk or washer. O Interactive 3D Graph Help 5 - 4- 1 - -1 -0.5 - -1 0.5 7-5 O O O Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help y 5 - 5 - 5 2 3 - -1 -0.5 -1 0.5 -1 0.5 -1 -0.5 -1 -2 -2 -3 --3 -5 -5 Need Help? Read It11. [-/1 Points] DETAILS SCALCET9 6.2.029. Three regions are defined in the figure. C (0, 4) B (1, 4) R2 R3 ly =4 Vx R1 y =4x X O A (1,0) Find the volume generated by rotating the given region about the specified line. R , about OA Need Help? Read It Watch It
