Antiderivatives And The Fundamental Theorem Of Calculus

10 Questions | Total Attempts: 119

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Antiderivatives And The Fundamental Theorem Of Calculus

This theory can be summed up as the theorem that links the concept of differentiating a function with the concept of integrating a function. In other words, the theorem shows that these 2 operations are fundamentally inverses of one another. Take our quiz to practice your knowledge about calculus and see how well you are doing.


Questions and Answers
  • 1. 
    What does the theorem imply?
    • A. 

      That the changes in a quantity over time adds up to the net change in quantity

    • B. 

      That the sum of infinitesimal changes in a quantity over time adds up to the net change in quantity

    • C. 

      That the addition in quantity over a small period of time adds up to the net change in quantity

    • D. 

      That a given function f(x) adds up to the net change in quantity

  • 2. 
    What does "summing up" correspond to?
    • A. 

      Fusion

    • B. 

      Integration

    • C. 

      Logarithm

    • D. 

      Cumulus

  • 3. 
    From what is the velocity function derived from?
    • A. 

      The position function

    • B. 

      The logarithm function

    • C. 

      Optics

    • D. 

      Cosinus

  • 4. 
    How can you sum up the theorem using a formula?
    • A. 

      Dx=dt

    • B. 

      Dx=v(t)dt

    • C. 

      Dt=v(x)dx

    • D. 

      Dt=vx

  • 5. 
    How many parts of the theorem are there?
    • A. 

      2

    • B. 

      3

    • C. 

      4

    • D. 

      5

  • 6. 
    What does the first part of the theorem deal with?
    • A. 

      Anti derivatives

    • B. 

      The derivative of an anti derivative

    • C. 

      Function f(x)

    • D. 

      Function lnx

  • 7. 
    What does the second part of the theorem deal with?
    • A. 

      Definite integrals

    • B. 

      The relationship between anti derivatives and definite integrals

    • C. 

      Anti derivatives

    • D. 

      Function f(x)

  • 8. 
    What does the corollary assume?
    • A. 

      The continuity on the whole interval

    • B. 

      The continuity on the function

    • C. 

      The continuity on the window of solutions

    • D. 

      The limits of the whole interval

  • 9. 
    What is the second part of the theorem called?
    • A. 

      The Newton-Leibniz axiom

    • B. 

      The Pythagoras axiom

    • C. 

      The Newton-Leibniz function

    • D. 

      The Newton-Leibniz theorem

  • 10. 
    What is the mean value theorem?
    • A. 

      It states that for a given planar arc between 2 endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its axe

    • B. 

      It states that for a given set of endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its endpoints

    • C. 

      It states that for a given planar arc between 2 endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its endpoints

    • D. 

      It states that for a given planar arc between 2 endpoints, there are at least 3 points at which the tangent to the arc is parallel to the secant through its endpoints

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