Understanding the Fundamental Theorem of Calculus:

• The Fundamental Theorem of Calculus has two parts that are inverse to each other.

  True
• What does the definite integral $\int_{a}^{b} f(x) dx$ equal according to the Fundamental Theorem?


  $F(b) - F(a)$
• Match the concept with its definition:

  Differentiation ↔️ Finds the rate of change of a function

  Integration ↔️ Finds the total accumulation of a function
• What is the antiderivative of x^2</latex>?

  $\frac{x^{3}}{3}$
• What is the first step in evaluating a definite integral using the Fundamental Theorem of Calculus (FTC)?

  Find the antiderivative
• The first part of the FTC states that the derivative of an integral gives back the original function.

  True
• Differentiation finds the rate of change of a function.


  True
• The definite integral of $\int_{1}^{3} x dx$ is equal to $\frac{x^{2}}{2}$ evaluated at the upper and lower bounds
• What does the Fundamental Theorem of Calculus link together?

  Differentiation and integration
• The derivative of the integral of a function is the original function itself.


  True
• The definite integral equals the difference of the antiderivative evaluated at the upper and lower bounds
• Steps to evaluate definite integrals using the Fundamental Theorem of Calculus:

  1️⃣ Find the antiderivative of the function

  2️⃣ Evaluate the antiderivative at the upper and lower bounds

  3️⃣ Subtract the values to find the definite integral
• When evaluating a definite integral, you must always include the constant of integration $+$$C$.


  False
• What does the first part of the Fundamental Theorem of Calculus state?

  $F'(x) =$$f(x)$
• What are differentiation and integration considered in relation to each other?

  Inverse operations
• What is the derivative of $F(x) =$$\int_{2}^{x} t^{2} dt$ according to the Fundamental Theorem of Calculus?


  $x^{2}$
• If F(x) = \int_{a}^{x} f(t) dt</latex>, then <latex>F'(x) = f(x)
• Differentiation and integration are inverse processes.
• What is the value of $\int_{1}^{3} x^{2} dx$ using the Fundamental Theorem of Calculus?


  $\frac{26}{3}$
• The definite integral is calculated by subtracting $F(a)$ from $F(b)$, where $a$ and $b$ are the lower and upper bounds
• The second part of the FTC calculates the definite integral by evaluating the antiderivative at the upper and lower limits
• The Fundamental Theorem of Calculus formalizes the relationship between differentiation and integration
• What does the Fundamental Theorem of Calculus link together?

  Differentiation and integration