6
Integration
542
6.4 CONCEPT QUESTIONS, page 437
1.
See the Fundamental of Calculus Theorem on page 429 in the text.
2.
See page 433 in the text.
a.
It measures the total income generated over the (
b
–
a
) days.
b.
( )
b
a
R t dt
∫
EXERCISES 6.4, page 437
1.
4
4
1
1
2
2
2(4
1)
6,
A
dx
x
=
=
=
−
=
∫
or 6
square units. The region is a rectangle
whose area is
3
⋅
2, or 6, square units.
2.
A
dx
x
=
=
=
− −
=
−
z
4
4
8
4
12
2
1
2
-1
(
)
,
or 12 sq
units. The region is a rectangle whose area is
4[2
−
(
−
1)] = 12 sq units.
3.
A
x dx
x
=
=
=
−
=
z
2
9
1
8
1
3
2
1
3
,
or 8 sq units.
The region is a parallelogram of area
(1/2)(3
−
1)(2 + 6) = 8 sq units.

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