Using Properties of Definite Integrals Given ∫ 4 8 f ( x ) d x = 12 and ∫ 4 8 g ( x ) d x = 5 , evaluate (a) ∫ 4 8 [ f ( x ) − g ( x ) ] d x (b) ∫ 4 8 [ 2 f ( x ) − 3 g ( x ) ] d x
Using Properties of Definite Integrals Given ∫ 4 8 f ( x ) d x = 12 and ∫ 4 8 g ( x ) d x = 5 , evaluate (a) ∫ 4 8 [ f ( x ) − g ( x ) ] d x (b) ∫ 4 8 [ 2 f ( x ) − 3 g ( x ) ] d x
Solution Summary: The author explains how to calculate the integral using the properties of the definite integral.
Using Properties of Definite Integrals Given
∫
4
8
f
(
x
)
d
x
=
12
and
∫
4
8
g
(
x
)
d
x
=
5
, evaluate
(a)
∫
4
8
[
f
(
x
)
−
g
(
x
)
]
d
x
(b)
∫
4
8
[
2
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.
f(x)= square root of 4x -x2
g(x)=square root of -48+16x-x2
h(x)=1-|x-13|
Evaluate the integrals of the functions graphed using the formulas for areas of triangles and circles. Enter the sum of all shaded areas in terms of π.
Applying reduction formulas Use the reduction formulas in evaluate the following integrals.
c. Evaluate the indefinite integrals by selecting an appropriate substitution. Remember to change the bounds for indefinite integrals. Solve c) ii.
Chapter 5 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY