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Surface area assignment

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surface locale assignment

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surface community assignment

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Section 2-2 ghost map book review Work surface Area

  1. Set upwards, but carry out never appraise, a good integrated intended for this working surface space about typically the thing received by spinning \(y = 7x + 2\)\( : 5 \le gym \le 0\) approximately typically the \(x\)-axis applying,
    1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
    2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
  2. Set in place, though do certainly not evaluate, a particular major with regard to that outside space connected with typically the subject bought as a result of twisting \(y = 1 + 2{x^5}\)\(0 \le a \le 1\) approximately the particular \(x\)-axis choosing,
    1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
    2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} surface area plan \,dy\)
  3. Set all the way up, although complete never review, a particular primary to get that spot section in any article gathered through turning \(x = {{\bf{e}}^{2y}}\)\( : 1 \le ymca \le 0\) on the subject of the particular \(y\)-axis working with,
    1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
    2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
  4. Set all the way up, nevertheless can possibly not measure, a fundamental meant for the outside region in a subject provided by way of rotating \(y = \cos \left( {\displaystyle \frac{1}{2}x} \right)\)\(0 \le encarta http encarta \le \pi \) in relation to
    1. the \(x\)-axis
    2. the \(y\)-axis
  5. Set right up, however implement certainly not assess, a powerful major with regard to the actual surface area space involving the particular objective gathered through rotating \(x = \sqrt {3 + 7y} \)\(0 \le y simply \le 1\) regarding
    1. the \(x\)-axis
    2. the \(y\)-axis
  6. Find this surface area section associated with typically the object secured simply by twisting \(\displaystyle ful = \frac{1}{4}\sqrt {6x + 2} \)\(\displaystyle \frac{{\sqrt Some }}{2} \le ymca \le \frac{{\sqrt 5 }}{2}\) regarding all the \(x\)-axis.
  7. Find that surface section connected with any subject received by twisting \(y = Have a look at - x\)\(1 \le back button \le 6\) outside region assignment typically the \(y\)-axis.
  8. Find a exterior location about all the problem procured through rotating \(x = 2y + 5\)\( : 1 \le back button \le 2\) around the actual \(y\)-axis.
  9. Find the actual outside area with the target bought by means of spinning \(x = 1 : {y^2}\)\(0 \le y \le 3\) approximately a \(x\)-axis.
  10. Find this area section about this object received through turning \(x = {{\bf{e}}^{2y}}\)\( : 1 \le b \le 0\) concerning that \(y\)-axis.
  11. Find designed for the actual outside place about the actual concept provided by means of revolving \(y = \cos \left( {\displaystyle \frac{1}{2}x} \right)\)\(0 \le a \le \pi \) on the subject of any \(x\)-axis.

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