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Stewart_Calc_7ET ch06sec01
MULTIPLE CHOICE
1. Find the area of the region bounded by the given curves.
a.
b.
c.
d.
e.
2. Sketch the region enclosed by the curves Find the
area of the region correct to two decimal places.
a.
b.
c.
d.
e.
f.
3. Find the area of the region bounded by the given curves.
a.
b.
c.
4
d.
2
e.
4. Graph the region between the curves and use your calculator to compute the area correct to five
decimal places.
a.
12.08127
b.
91.504
c.
3.141257
d.
3.66016
e.
18.3008
5. Find the area of the region bounded by the given curves.
a.
b.
None of these
c.
d.
e.
6. Find the number b such that the line divides the region bounded by the curves
and into two regions with equal area.
a.
b.
c.
d.
e.
7. Find the area of the shaded region.
a.
b.
c.
d.
y=x+ 4
y–x=2–4
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
y
112
3
56
3
112
9
224
3
8. Find the area of the shaded region.
a.
7
b.
c.
d.
9. Sketch the region bounded by the graphs of the given equations and find the area of their
region.
, ,
a.
c.
y =
y = x –
–6 x2+ 6x
x/_
`
1 2 x
1
2
3
–1
y
7
12
1
6
7
6
b.
d.
10. Sketch the region bounded by the graphs of the given equations and find the area of their region.
, ,
a.
c.
1–1 x
1
–1
y
1–1 x
1
–1
y
1–1 x
1
–1
y
1–1 x
1
–1
y
b.
d.
11. Sketch the region bounded by the graphs of the given equations and find the area of that
region.
y = sec2 x + 6, y = 8, x = – , x =
a.
c.
10 x
10
–10
y
−16
3
10 x
10
–10
y
32
3
10 x
10
–10
y
−32
3
10 x
10
–10
y
16
– 2
– 1
b.
+ 8
d.
–
12. Use integration to find the area of the triangle with the given vertices.
(0, 0), (1, 7), (4, 2)
a.
b.
26
c.
28
d.
1–1 x
2
4
6
8
y
1–1 x
2
4
6
8
y
1–1 x
2
4
6
8
y
1–1 x
2
4
6
8
y
13
2
13
13. Sketch the region enclosed by . Find t he area of the region.
a.
b.
c.
d.
e.
14. Find the area of the region bounded by the parabola , the tangent line to this parabola
at , and the x axis.
a.
b.
c.
d.
e.
1. Sketch the region enclosed by Find the area of the region.
32
3
32
3
1
12
2. Find the values of c such that the area of the region bounded by the parabolas
is .
3. Find the area of the region bounded by the curves.
4. Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows
the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the
Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten
seconds.
5. Find the area of the region bounded by the curves.
SHORT ANSWER
1. Sketch the region bounded by the graphs of the given equations and find the area of that
region.
, , ,
2. Sketch the region bounded by the graphs of the given equations and find the area of that
region.
y = + 4, y = 2x + 1
3. Sketch the region bounded by the graphs of the given equations and find the area of that
region.
y = sin 2x, y = 7cos x, x = , x =
4. Use a graphing utility to (a) plot the graphs of the given functions and (b) find the x-
coordinates of the points of intersection of the curves. Then find an approximation of the area
of the region bounded by the curves using the integration capabilities of the graphing utility.
Round answers to two decimal places.
y = 3 , y = 5 –
