Calculus: Integrals and Antiderivatives
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Questions and Answers

What is the process of passing from the derivative of a function to the function itself?

  • Antidifferentiation (correct)
  • Differentiation
  • Integration
  • Calculation

    • What symbol denotes the operation of antidifferentiation?

  • ∫ (correct)
  • dy
  • f(x)
  • dx

    • What is the function f called in the context of antidifferentiation?

  • The function
  • The antiderivative
  • The derivative
  • The integrand (correct)

    • What is the expression F(x) + C called?

    <p>The general antiderivative</p> Signup and view all the answers

    What does dx help identify in an integral?

    <p>The variable of integration</p> Signup and view all the answers

    What is the relationship between integration and differentiation?

    <p>They are opposite operations</p> Signup and view all the answers

    What is the formula for the power rule in integral calculus?

    <p>∫ 𝑥 𝑛 𝑑𝑥 = 𝑥 𝑛+1 𝑛+1 +C</p> Signup and view all the answers

    What is the condition for the power rule to be applied?

    <p>n ≠ −1</p> Signup and view all the answers

    What is the result of differentiating 𝑥 𝑛+1 𝑛+1 +C?

    <p>𝑥 𝑛</p> Signup and view all the answers

    What is the formula for the antiderivative of (ax + b)𝑛?

    <p>1 𝑎(𝑛+1) (ax + b)𝑛+1 + 𝐶</p> Signup and view all the answers

    What is the result of applying the power rule to ∫(2𝑥 − 1)3 𝑑𝑥?

    <p>1 8 (2𝑥 − 1)4 + 𝐶</p> Signup and view all the answers

    What is the result of applying the power rule to ∫ 𝑡 3 𝑑𝑡?

    <p>2 𝑡 4 + 𝐶</p> Signup and view all the answers

    What is the term for the function F(x) in the equation ∫f(x)dx = F(x) + C?

    <p>Antiderivative</p> Signup and view all the answers

    What is the value of the derivative of a constant?

    <p>0</p> Signup and view all the answers

    What is the formula for the indefinite integral of x^n?

    <p>∫x^n dx = x^(n+1) / (n+1) + C</p> Signup and view all the answers

    What is the term for the constant C in the equation ∫f(x)dx = F(x) + C?

    <p>Constant of Integration</p> Signup and view all the answers

    What is the antiderivative of f(x) = 2x?

    <p>x^2 + C</p> Signup and view all the answers

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