Each antiderivative of an nth-degree polynomial function is an (n + 1)th-degree polynomial function.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 59E
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Please solve 74 and 76

True or False? In Exercises 73 and 74, determine whether
the statement is true or false. If it is false, explain why or give
an example that shows it is false.
73. The antiderivative of f(x) is unique.
74. Each antiderivative of an nth-degree polynomial function is an
(n + 1)th-degree polynomial function.
75. Proof Let s(x) and c(x) be two functions satisfying
s'(x) = c(x) and c'(x) = - s(x) for all x. If s(0) = 0 and
c(0) = 1, prove that [s(x)]² + [c(x)]? = 1.
|
76. Think About It Find the general solution of
f'(x) = – 2x sin x2.
Transcribed Image Text:True or False? In Exercises 73 and 74, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. 73. The antiderivative of f(x) is unique. 74. Each antiderivative of an nth-degree polynomial function is an (n + 1)th-degree polynomial function. 75. Proof Let s(x) and c(x) be two functions satisfying s'(x) = c(x) and c'(x) = - s(x) for all x. If s(0) = 0 and c(0) = 1, prove that [s(x)]² + [c(x)]? = 1. | 76. Think About It Find the general solution of f'(x) = – 2x sin x2.
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