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Chapter 4: Definite Integrals

Expert-verified
Calculus
Pages: 315 - 406
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Illustration

734 Questions for Chapter 4: Definite Integrals

  1. h

    Found on Page 338

  2. Read the section and make your own summary of the material

    Found on Page 351

  3. Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counter example.

    Found on Page 338

  4. Consider the area between the graph of a positive function f and the x-axis on an interval [a, b]. Explain why the upper sum approximation for this area with n = 8 boxes must be smaller than or equal to the upper sum approximation with n = 4 boxes. It may help to sketch some examples.

    Found on Page 339

  5. Suppose you wanted to calculate the upper sum approximation for the area between the graph of f(x) = (x − 1)2 and the x-axis from x = 0 to x = 2. List all of the values Mk used for (a) n = 2 rectangles, (b) n = 3 rectangles, and (c) n = 4 rectangles. Sketch graphs of your rectangles to illustrate your answers

    Found on Page 339

  6. f(x)=x2-x-1,g(x)=5-x2,[-2,3]

    Found on Page 386

  7. Shade in the regions between the two functions shown here on the intervals (a) [-2,3]; (b) [-1,2]and (c)[1,3]. Which of these regions has the largest area? The smallest?

    Found on Page 384

  8. Is integration the opposite of differentiation? In what sense do derivatives “undo” integrals? In what sense do integrals “undo” derivatives? In what sense do they not? In your answer, be sure to consider indefinite integrals, definite integrals, and accumulation functions defined by integrals.

    Found on Page 405

  9. The Fundamental Theorem of Calculus: Why is the Fundamental Theorem of Calculus so fundamental? What does it allow us to calculate, and what concepts does it relate? Give an overview outline of the proof of this important theorem

    Found on Page 405

  10. a

    Found on Page 398

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