Calculus: Integrals and Antiderivatives
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Questions and Answers

What is the process of finding the antiderivative of a function called?

  • Differentiation
  • Antidifferentiation (correct)
  • Derivation
  • Integration

    • What is the symbol that denotes the operation of antidifferentiation?

  • ∫ (correct)
  • Δ
  • ∂
  • F

    • What is the term for the function being integrated?

  • Antiderivative
  • Derivative
  • Integrand (correct)
  • Function

    • What is the purpose of the dx in the integral notation?

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

    What is the general form of an antiderivative of a function f(x)?

    <p>F(x) + C</p> Signup and view all the answers

    What is the relationship between integration and differentiation?

    <p>Integration is the inverse operation of differentiation</p> Signup and view all the answers

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

    <p>∫x^2 dx = (x^3)/3 + C</p> Signup and view all the answers

    What is the derivative of the antiderivative F(x) = x^3 + C?

    <p>F'(x) = 3x^2</p> Signup and view all the answers

    What is the indefinite integral of f(x) = 2x?

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

    What is the purpose of the constant C in the antiderivative F(x) = x^n + C?

    <p>It is an arbitrary constant.</p> Signup and view all the answers

    What is the relation between F(x) and f(x) if F'(x) = f(x)?

    <p>F(x) is the antiderivative of f(x).</p> Signup and view all the answers

    What is the Power Rule formula for finding the indefinite integral of 𝑥ⁿ with respect to 𝑥?

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

    What is the condition for applying the Power Rule to find the antiderivative of 𝑥ⁿ?

    <p>𝑛 cannot be -1</p> Signup and view all the answers

    What is the formula for finding 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 find the antiderivative of (2𝑥 - 1)³?

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

    What is the purpose of the constant 𝐶 in the Power Rule formula?

    <p>To represent the arbitrary constant of the antiderivative</p> Signup and view all the answers

    What is the name of the rule that allows us to find the indefinite integrals of various functions like polynomials and functions involving roots?

    <p>Power Rule</p> Signup and view all the answers

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