a.
To explain: how can use the derivative of F(x) + C to confirm the
a.
Answer to Problem 78E
If the derivative of F(x) + C is equal to f(x) then the integration was performed correctly.
Explanation of Solution
Given information: Suppose that
Calculation:
If the derivative of F(x) + C is equal to f(x) then the integration was performed correctly.
b.
To explain: how can use a slope field of f and the graph of y = F(x) to support evaluation of the integral.
b.
Answer to Problem 78E
The slope field generated by f ( x ) should generate all curves in the family y = F(x) + C .
Explanation of Solution
Calculation:
The slope field generated by f ( x ) should generate all curves in the family y = F(x) + C .
c.
To explain: how can use the graph of
c.
Answer to Problem 78E
Explanation of Solution
Calculation:
d.
To explain: how can use a table of values for
d.
Answer to Problem 78E
Use the table of values to evaluate
Explanation of Solution
Calculation:
Use the table of values to evaluate
e.
To explain: how can use graph of f and NDER of F(x) to support evaluation of the integral.
e.
Answer to Problem 78E
The graph of f and NDER of F(x) should correspond exactly to the graph y = f(x).
Explanation of Solution
Calculation:
The graph of f and NDER of F(x) should correspond exactly to the graph y = f(x).
f.
To illustrate: parts (a )-(e) for
f.
Answer to Problem 78E
Explanation of Solution
Calculation:
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic
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