Learning Materials
Features
Discover
Chapter 4: Q. 56 (page 353)
Use the definition of the definite integral as a limit of Riemann sums to prove Theorem 4.12(a): For any function f and real number a,
The theorem 4.12(a) is proved.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
Suppose f is a function whose average value on is
and whose average rate of change on the same in-
terval is . Sketch a possible graph for f . Illustrate the
average value and the average rate of change on your
graph of f .
Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.
Shade in the regions between the two functions shown here on the intervals (a) [鈭�2, 3]; (b) [鈭�1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?
Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercises 21鈥�26, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine