Fundamental Theorem of Calculus and Integration Methods
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Questions and Answers

What is the fundamental theorem of calculus used for?

  • To find the derivative of a function
  • To calculate the limit of a sequence
  • To solve systems of differential equations
  • To find the area under a curve (correct)

    • What does the integral of a function represent?

  • The minimum value of the function
  • The slope of the function
  • The average value of the function (correct)
  • The maximum value of the function

    • When does the substitution method need to be used in integration?

  • When integrating trigonometric functions
  • When working with improper integrals
  • When the integrand is a product of functions (correct)
  • When finding the definite integral

    • Which of the following is NOT a method for evaluating indefinite integrals?

    <p>Rolle's theorem</p> Signup and view all the answers

    In integral calculus, which of the following is a valid application of the mean value theorem?

    <p>Finding the average value of a function on a given interval</p> Signup and view all the answers

    When evaluating integrals involving trigonometric functions, which substitution technique is most appropriate for expressions containing $a^2 - x^2$?

    <p>$x = a \cos(\theta)$</p> Signup and view all the answers

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