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.
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.)
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
Range of the function f(x) = 2 sin(1/x) is
O 1]
O 1-2, 2]
O 12,-1)
O (-1, 2]
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