Area and volume practice

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Area and volume practice

  1. 1. Review-Unit 6• Area – With respect to the x-axis – With respect to the y-axis (Careful with y-axis rotations, everything must be in terms of y!!!) – Inverse (gets everything back in terms of x) • Useful when you see x= • Also helpful with square root functions sometimes• Volume – Disk πr2h (h is typically dx/dy) Careful with y-axis rotations, everything – Washer (disk with a hole) πr2h must be in terms of y!!! – Shell 2πrhw (w is typically dx/dy) • Useful with y-axis rotations or x=# line rotations (everything is in terms of x)
  2. 2. .1. Find the area between thegraph of y = x − x + 2 and y = 0 3in [1,3]. Graphing by hand requiressynthetic division to find roots.Answers on last slide!
  3. 3. .2. Find the area bounded by thegraph of y = x + 2 x − 3 and y=0. 2
  4. 4. .3. Find the area between thegraph of y = ( x − 1) and y = x − 1 3
  5. 5. .4. Find the area between thegraph of and y = − x + 6 and y=0 y= x
  6. 6. .5. Find the area between thegraph of y = x − 1 and x = 3 − y 2
  7. 7. .6. Find the volume of the regionbounded by the curves y = x andy = x and rotated about the y-axis
  8. 8. .7. Find the volume of the regionbounded by the curves y = x / 27 and 2y = x and rotated about the x-axis
  9. 9. .8. Find the volume of the regionbounded by the curves y = x + 1 , x=0 2and y=0 and x=2 rotated about thex-axis
  10. 10. .9. Find the volume of the regionbounded by the curves y = 4 − x , x=0 2and y=0 (Q I) rotated about the x-axis
  11. 11. .10. Find the volume of the regionbounded by the curves y = x and y = x 3(Q I) rotated about the y-axis
  12. 12. .11. Find the volume of the regionbounded by the curves y = x and x = 8(Q I) rotated about the line x=8
  13. 13. .12. Find the volume of the regionbounded by the curves y = x and 2y=2x (Q I) rotated about the y-axis
  14. 14. .13. Find the volume of the regionbounded by the curves y = x + 1 , 2x=0, x=5 and y=0 (Q I) rotated aboutthe y-axis
  15. 15. Answers:1) 20 u2 8) 206∏/15 u32) 32/3 u2 9) 53.62 u33) ½ u2 10) .18 u34) 7.33 u2 11) 303.3 u35) 9/2 u2 12) 8∏/3 u36) 2∏/15 ≈ .419 u3 13) 675∏/2 u37) 243∏/10 u3

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