Mathematics Quiz: Integration Methods

7 Questions

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Mathematics Quiz: Integration Methods

Integration by reverse power rule rewriting and properties of integrals reverse chain rule (substitution)


Questions and Answers
  • 1. 
    Which statement best describes the meanings of definite and indefinite integrals?
    • A. 

      Definite and indefinite integrals represent areas under curves. Definite integrals are for a specific interval, while indefinite integrals are accumulation functions.

    • B. 

      Definite integrals represent backwards differentiation while indefinite integrals represent limits of Riemann sums.

    • C. 

      Definite integrals represent areas under curves while indefinite integrals represent families of antiderivatives.

    • D. 

      Definite integrals represent families of antiderivatives while indefinite integrals represent specific antiderivatives.

  • 2. 
    Which plan(s) could be followed to integrate 
    • A. 

      First rewrite the integrand in general form and then apply the power rule to each term.

    • B. 

      Raise the power to 4 and then divide by 4.

    • C. 

      Distribute the exponent to the two terms and then apply the power rule to each term.

    • D. 

      Substitute u=1–x and then apply the power rule to integrate u^3.

  • 3. 
    Now carry out this integration:  Is the derivative of your result equivalent to the integrand?
    • A. 

      Yes

    • B. 

      No

  • 4. 
    What would be a useful substitution to perform this integration? 
    • A. 

      U=2x^2

    • B. 

      W=x^2

    • C. 

      Z=4+3x^3

    • D. 

      M=(4+3x^3)^6

  • 5. 
    Now carry out this integration:  Is the derivative of your result equivalent to the integrand?
    • A. 

      Yes

    • B. 

      No

  • 6. 
    Which two scientists were involved in the discovery of "the Fundamental Theorem of Calculus?"
    • A. 

      Sir Isaac Newton

    • B. 

      Albert Einstein

    • C. 

      Gottfried Wilhelm Leibniz

    • D. 

      Srinivasa Ramanujan

  • 7. 
    Who introduced the notation for the indefinite integral?
    • A. 

      Jacob Bernoulli

    • B. 

      Joseph Fourier

    • C. 

      Gottfried Leibniz

    • D. 

      Georg Riemann