298 STEP 4. Review the Knowledge You Need to Score High
- (See Figure 12.9-2.)
Set 2x− 6 =0;x=3 and
f(x)=
{
2 x−6ifx≥ 3
−(2x−6) ifx< 3.
A=
∫ 3
0
−(2x−6)dx+
∫ 4
3
(2x−6)dx
=
[
−x^2 + 6 x
] 3
0 +
[
x^2 − 6 x
] 4
3
=
[
−(3)^2 +6(3)
]
− 0 +
[
42 +6(4)
]
−
[
32 −6(3)
]
= 9 + 1 = 10
043
y
x
y = 2x–6
x = 0 x = 4
Figure 12.9-2
- (See Figure 12.9-3.)
Length ofΔx 1 =
5 − 1
4
=1.
Area of RectI=f(2)Δx 1 =
1
2
(1)=
1
2
.
Area of RectII=f(3)Δx 2 =
1
3
(1)=
1
3
.
Area of RectIII=f(4)Δx 3 =
1
4
(1)=
1
4
.
Area of RectIV=f(5)Δx 4 =
1
5
(1)=
1
5
.
Total Area=
1
2
+
1
3
+
1
4
+
1
5
=
77
60
.
I II
III IV
023451
y
x
f(x) =x^1
Not to Scale
Figure 12.9-3
- (See Figure 12.9-4.)
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 12.9-4