8/2/2019 Assignment Integration

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Assignment Integration M.Y.

Find the indefinite integrals.

a)

b) c) d) e) f) g) h) i) j)

k)

l)

m) n) o) p) q)

r) s)

Sketch the curve ! " and line ! " in one diagram.Find the area of the region enclosed by the curve! " and the line ! " #

The diagram shows the curve ! " and the line ! " # Given that PQ isparallel to the y-axis, find the

a) coordinate of Qb) area of the shaded region.

The diagram shows part of the curve! " # PQ isthe tangent to the curve at P. Find

a) coordinate of Qb) area of the shaded region.

8/2/2019 Assignment Integration

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Assignment Integration M.Y.

The diagram shows part of the curve

! " . Find area of the shaded region.

State the coordinate of the point P and find the area of the shaded region.

The diagram shows part of the curve! " # Find the area of the shadedregion.

The diagram shows the curve ! " which intersects the x-axis at P and the y- axis atQ. Find the

a) coordinates of P and Qb) ratio of the area of shaded region A to B.

8/2/2019 Assignment Integration

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Assignment Integration M.Y.

Find the area of the shaded region of the diagram below:

The diagram shows part of the curve! " $# Find thea) area of region Ab) value of p where area of B and C is the same.

The diagram shows the curve ! " # The shaded regionis bounded by the curve, the y-axis and the line y = 8.Find the volume of the solid generated when this shadedregion is rotated completely about the y-axis, giving your

answers in terms of#

8/2/2019 Assignment Integration

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Assignment Integration M.Y.

Find in terms ofa, the volume generated when theshaded region is rotated through 360 about the x-axis.

The diagram shows part of the curve% !

" # Find the volume of the solidgenerated when this shaded region is rotated through360 about the x-axis.

Find the volume of the solid generated when theshaded region is rotated through 360 about the y-axis.

Find the volume of the solid generated when this shadedregion is rotated through 4 right angles about the y-axis.

Find the volume of the solid generated when thisshaded region is rotated through 360 about the x-axis.

8/2/2019 Assignment Integration

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Assignment Integration M.Y.

Find the volume of the solid generated for the following diagrams when the shadedregions are rotated through 4 right angles about the x-axis.