(2015-16 Spring Semester) Math 1014 Tutorial 2 - (2015-16...

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(2015-16 Spring Semester) Math 1014 Tutorial 2 (T4 & 5) Page | 1(1)Method of Slicing (a) Cross-sectional Area A(x) perpendicular to the x-axis, The Volume 𝑽 = ∫ 𝑨(?)???(b) Cross-sectional Area A(y) perpendicular to the y-axis, The Volume 𝑽 = ∫ 𝑨(?)???(2) Disk / Washer Method (a)Revolved about the x-axisThe Volume = ∫ 𝝅?????= ∫ 𝝅(?(?))?????. (b)Revolved about the y-axisThe Volume = ∫ 𝝅?????= ∫ 𝝅(?(?))?????. (a)Revolved about the y-axisThe Volume = ∫ ?𝝅?(?(?) − ?(?))???. (b)Revolved about the x-axisThe Volume = ∫ ?𝝅?[?(?) − ?(?)]???. ??, ?, ?(3) Cylindrical Shell Method , ?, ?
(2015-16 Spring Semester) Math 1014 Tutorial 2 (T4 & 5) Page | 2Example Solution: (4) Volume of Revolution about an axis other than the x-axis and y-axis (a) Revolving about the line ? = ?Let ? = ?(?)be a function continuous on [a, b] and let Sbe the region bounded by the curve ? = ?(?)and the line ? = ?? = ?and ? = ?. Then the volume of the solid generated by revolving the region Sone complete revolution about the line ??.,
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