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
Graphing Inverse Functions
Each of Exercises 11–16 shows the graph of a function y = ƒ(x).Copy the graph and draw in the line y = x. Then use symmetry withrespect to the line y = x to add the graph of ƒ -1 to your sketch. (It isnot necessary to find a formula for ƒ -1.) Identify the domain andrange of ƒ -1.
Chapter 5 Solutions
WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term
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