Using Properties of Definite Integrals In Exercises 7 and 8, use the values ∫ 0 5 f(x) dx = 6 and ∫ 0 5 g ( x ) d x = 2 to evaluate each definite integral. ∫ 0 5 [ f ( x ) + g ( x ) ] d x ( b ) ∫ 0 5 [ ( f ( x ) − g ( x ) ] d x (c) ∫ 0 5 − 4 f ( x ) d x ( d ) ∫ 0 5 [ ( f ( x ) − 3 g ( x ) ] d x
Using Properties of Definite Integrals In Exercises 7 and 8, use the values ∫ 0 5 f(x) dx = 6 and ∫ 0 5 g ( x ) d x = 2 to evaluate each definite integral. ∫ 0 5 [ f ( x ) + g ( x ) ] d x ( b ) ∫ 0 5 [ ( f ( x ) − g ( x ) ] d x (c) ∫ 0 5 − 4 f ( x ) d x ( d ) ∫ 0 5 [ ( f ( x ) − 3 g ( x ) ] d x
Solution Summary: The author explains how to calculate the definite integral of function displaystyle
Using Properties of Definite Integrals In Exercises 7 and 8, use the values
∫
0
5
f(x) dx = 6 and
∫
0
5
g
(
x
)
d
x
=
2
to evaluate each definite integral.
∫
0
5
[
f
(
x
)
+
g
(
x
)
]
d
x
(
b
)
∫
0
5
[
(
f
(
x
)
−
g
(
x
)
]
d
x
(c)
∫
0
5
−
4
f
(
x
)
d
x
(
d
)
∫
0
5
[
(
f
(
x
)
−
3
g
(
x
)
]
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Write the definition of the definite integral of a function from a to b. (b) What is the geometric interpretation of f(x) dx if f(x) > 0? (c) What is the geometric interpretation of f(x) dx if f(x) takes on both positive and negative values? Illustrate with a diagram
K
Use the definition of the definite integral to evaluate
f(x²-2) dx.
ju
(x²-2) dx = (Type an integer or a simplified fraction.)
Range of the function f(x) = 2 sin(1/x) is
O 1]
O 1-2, 2]
O 12,-1)
O (-1, 2]
Chapter 5 Solutions
Calculus: An Applied Approach (MindTap Course List)
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