MA 3972-MA-Book April 11, 2018 16:1
Areas and Volumes 307
- (See Figure 13.8-4.)
Trapezoid Rule =
b−a
2 n
(
f(a)+ 2 f(x 1 )
+ 2 f(x 2 )+ f(b)
)
.
A=
3 − 0
2(3)
(f(0)+ 2 f(1)+ 2 f(2)+f(3))
=
1
2
(1+ 4 + 10 +10)=
25
2
y
x
y = x^2 + 1
Not to
scale
0123
Figure 13.8-4
- (See Figure 13.8-5.)
A=
∫ 4
0
(√
x−(−x)
)
dx
=
∫ 4
0
(
x^1 /^2 +x
)
dx=
[
2 x^3 /^2
3
+
x^2
2
] 4
0
=
(
2(4)^3 /^2
3
+
42
2
)
− 0
=
16
3
+ 8 =
40
3
04
y = –x
x = 4
y
x
y = x
Figure 13.8-5
- (See Figure 13.8-6.)
Intersection points: 4=y^2 ⇒y=±2.
A=
∫ 2
− 2
(
4 −y^2
)
dy=
[
4 y−
y^3
3
] 2
− 2
=
(
4(2)−
23
3
)
−
(
4(−2)−
(−2)^3
3
)
=
(
8 −
8
3
)
−
(
− 8 +
8
3
)
=
16
3
+
16
3
=
32
3
y
0 x
2
x = y^2
x = 4
Figure 13.8-6
