Calculus: Integrals and Antiderivatives

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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?

To identify the variable of integration Signup and view all the answers

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

F(x) + C Signup and view all the answers

What is the relationship between integration and differentiation?

Integration is the inverse operation of differentiation Signup and view all the answers

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

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

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

F'(x) = 3x^2 Signup and view all the answers

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

∫2x dx = x^2 + C Signup and view all the answers

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

It is an arbitrary constant. Signup and view all the answers

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

F(x) is the antiderivative of f(x). Signup and view all the answers

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

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

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

𝑛 cannot be -1 Signup and view all the answers

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

1 𝑎(𝑛+1) (𝑎𝑥 + 𝑏)ⁿ⁺¹ + C Signup and view all the answers

What is the result of applying the Power Rule to find the antiderivative of (2𝑥 - 1)³?

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

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

To represent the arbitrary constant of the antiderivative 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?

Power Rule Signup and view all the answers

Calculus: Integrals and Antiderivatives

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