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Problem 78

True or False? In Exercises $73-78$ , determine w…

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University of Delaware
Problem 77

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
$$f^{\prime}(x)=g(x),$ then $\int g(x) d x=f(x)+C$$

Answer

True

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. $\int f(x) g(x) d x=\left(\int f(x) d x\right)\left(\int g(x) d x\right)$ True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $F(x)$ and $G(x)$ are antiderivatives of $f(x),$ then $$F(x)=G(x)+C$$ True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $f^{\prime}(x)=g^{\prime}(x),$ then $f(x)=g(x)$ True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $f(x)=-g(x)+b,$ then $f^{\prime}(x)=-g^{\prime}(x)$ True or False? In Exercises $83 - 86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $$\int _ { a } ^ { b } [ f ( x ) - g ( x ) ] d x = A$$ then $$\int _ { a } ^ { b } [ g ( x ) - f ( x ) ] d x = - A$$ True or False? In Exercises $73-76$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $$\lim _{x \rightarrow c} f(x)=L,$ then $f(c)=L$$
Chapter 4
Integration
Section 1
Antiderivatives and Indefinite Integration
Calculus of a Single Variable


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