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MATH119
WEEK 8
RECITATION QUESTIONS
1. Find the area of the shaded region
2. Sketch the region enclosed by the given curves.Decide whether to integrate with recpect to
x or y.Draw a typical approximating rectangle and label its height and width.Then ﬁnd the
area of the region.
a
)
x
= 2
y
2
,
x
+
y
= 1
b
)
x
= 1

y
2
,
x
=
y
2

1
3. Use calculus to ﬁnd the area of the triangle with the given vertices.
(0
,
0)
,
(2
,
1)
,
(

1
,
6)
4. Find the volume of the solid obtained by rotating the region bounded by the given curves
about the speciﬁed line.Sketch the region,the solid,and a typical disk or washer.
a
)
y
=
x
2
,
y
2
=
x
; about the
x
axis
b
)
y
2
=
x ,
x
= 2
y
; about the
y
axis
c
)
y
=
x ,
y
=
√
x
; about
y
= 1
5. Refer to the ﬁgure and ﬁnd the volume generated by rotating the given region about the
speciﬁed line.
1
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)
R
1
about AB
b
)
R
2
about OC
6. Find the volume common to two spheres,each with radius r,if the centre of each sphere lies
on the surface of the other sphere.
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This note was uploaded on 03/31/2010 for the course MATHEMATIC 119 taught by Professor Muhiddinuğuz during the Fall '08 term at Middle East Technical University.
 Fall '08
 muhiddinuğuz
 Math, Calculus, Geometry

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