Integrating Even and Odd Functions In Exercises 61–64, evaluate the definite integral using the properties of even and odd functions. See Example 8 . ∫ − 1 1 ( 2 t 5 − 2 t ) d t
Integrating Even and Odd Functions In Exercises 61–64, evaluate the definite integral using the properties of even and odd functions. See Example 8 . ∫ − 1 1 ( 2 t 5 − 2 t ) d t
Solution Summary: The author explains how to calculate the definite integral of function displaystyle
Integrating Even and Odd Functions In Exercises 61–64, evaluate the definite integral using the properties of even and odd functions. See Example 8.
∫
−
1
1
(
2
t
5
−
2
t
)
d
t
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.
In Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see.
63. a. y = tan-1 (tan x) b. y = tan (tan-1 x)
64. a. y = sin-1 (sin x) b. y = sin (sin-1 x)
65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)
In Exercises 73–78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5
5. DISCUSS: Solving an Equation for an Unknown FunctionIn Exercises 69–72 of Section 2.7 you were asked to solveequations in which the unknowns are functions. Now thatwe know about inverses and the identity function (see Exercise 104), we can use algebra to solve such equations. Forinstance, to solve f g h for the unknown function f, weperform the following steps:
Chapter 5 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
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