Calculus Applications of Integration Page
19
Applications of Integration Day 5
First idea:
Draw
y
=
x
2
on the axes below.
Pick a point on the curve and label it:
P (x, y).
a) Draw the line y = –1 and find the
distance d from the point P to the line
b)
Draw the line y = 4
and find the
distance d from the point P to the
line
c)
Draw the line x = –1 and find the distance d from the point P to the line
d)
Draw the line x = 3 and find the distance d from the point P to the line
Second idea:
Review area formulas
Circle
Semicircle
Square
Isosceles Right triangle
Equilateral triangle
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Third idea:
Consider the solids we have been working with up to this point.
Suppose we sliced
the solid and pulled out a cross section – what would it look like?
Look at the volume formula – how could this formula be viewed in terms of the
crosssectional area
Consider another type of solid.
This solid is not formed by rotation of a region
about a line.
Considering a region as its base, then describing its crosssectional
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 Spring '10
 John
 Calculus, triangle, Circle Semicircle Square

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