AP Calculus Chapter 7 (Disk and Shell Method)
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Find the functions
f(x)= x + 1; g(x)= (x  1)^{2}

area of the shaded region
(x+1)(x1)
^{2 }dx

volume of region rotated around the x axis
π
(x+1)
^{2 }(x1)
^{2}dx

volume of the region rotated around the y axis
2π
x[(x+1)(x1)
^{2}]dx

Volume of the region rotated around the line y=8
π
[8(x1)2]
^{2}[8(x+1)]
^{2}dx

volume of the region rotated around y=4
π
[(x+1)+4]
^{2}[(x1)
^{2}+4)
^{2}dx

Volume of the region rotated around x=3
2π
(x+3)[(x+1)(x1)
^{2}]dx

volume of the region rotated around x=11
2π
(11x)[(x+1)(x1)
^{2}]dx

volume of the cross section of the region formed by semicircles
(π/8)
[(x+1)(x1)
^{2}]
^{2}dx

Volume of cross section of the region formed by equilarteral triangles

Volume of cross section of the region formed by right isosceles tringles where the leg is the base

volume of cross section of the region formed by right isosceles triangles where the hypotenuse is the base

volume of cross section of the region formed by squares

Find the functions in terms of y

area of the shaded region

volume of region rotated around the x axis

volume of the region rotated around the y axis

volume of the region rotated around the line y=8

volume of the region rotated around y=4

volume of the region rotated around x=3

volume of the region rotated around x=11

volume of cross section of the region formed by semicircles

volume of cross section of the region formed by equilateral triangles

volume of cross section of the region formed by right isosceles triangles where the leg is the base

volume of cross section of the region formed by right isosceles triangles where the hypotenuse is the base

volume of cross section of the region formed by squares