5128_Ch07_pp378-433

Section 7.2 Areas in the Plane 395
Quick Review 7.2 (For help, go to Sections 1.2 and 5.1.)
In Exercises 1–5, find the area between the x-axis and the graph of
the given function over the given interval.
1. y sin x over 0, p 2
2. y e 2x over 0, 1 1 2 (e 2 1) 3.195
3. y sec 2 x over p4, p4 2
4. y 4x x 3 over 0, 2 4
5. y 9 x 2 over 3, 3 9p/2
In Exercises 6–10, find the x- and y-coordinates of all points where
the graphs of the given functions intersect. If the curves never
intersect, write “NI.”
6. y x 2 4x and y x 6 (6, 12); (1, 5)
7. y e x and y x 1 (0, 1)
8. y x 2 px and y sin x (0, 0); (p, 0)
2x
9. y x
2
and y x
1
3 (1, 1); (0, 0); (1, 1)
10. y sin x and y x 3
(–0.9286, –0.8008); (0, 0); (0.9286, 0.8008)
Section 7.2 Exercises
In Exercises 1–6, find the area of the shaded region analytically.
1. y
p/2
4. y
4/3
1 x 12y 2 12y 3
1 y 1
y cos 2 x
x
0 –2
x 2y 2 2y
x
0
1
5. y
128/15
2. y
4p/3
y
1
– sec 2 t 2
2
(–2, 8)
8
(2, 8)
–3 –
1
0
–3
t
y x 4 2x 2
y 4 sin 2 t
–2
–1
–1
y 2x 2 2
1
x
–4
NOT TO SCALE
6. y
22/15
3. y
1/12
1
y x 2
1
x y 3
(1, 1)
–1
0
1
x
x y 2
0 1
x
–2
y –2x 4