Fundamental Theorem of Calculus Part 2 Worksheets with Solutions.

📚 Topic Summary

The Fundamental Theorem of Calculus Part 2 provides a method for evaluating definite integrals. It states that if $F(x)$ is an antiderivative of $f(x)$, then the definite integral of $f(x)$ from $a$ to $b$ is equal to $F(b) - F(a)$. In simpler terms, you find the antiderivative of the function, plug in the upper and lower limits of integration, and subtract the results. This theorem simplifies the process of calculating areas under curves significantly. 😊

Essentially, the Fundamental Theorem of Calculus Part 2 bridges the connection between differentiation and integration, showing that they are inverse processes. Applying this theorem correctly involves finding the antiderivative accurately and carefully evaluating it at the limits of integration. Let’s practice this with a fun worksheet!

🧠 Part A: Vocabulary

Match the term with its definition:

1. Antiderivative
2. Definite Integral
3. Integration
4. Limits of Integration
5. Fundamental Theorem of Calculus Part 2

1. The process of finding the area under a curve.
2. The upper and lower bounds of an integral.
3. A function whose derivative is a given function.
4. A theorem that connects differentiation and integration.
5. An integral with defined upper and lower limits, resulting in a numerical value.

(Answers: 1-3, 2-5, 3-1, 4-2, 5-4)

📝 Part B: Fill in the Blanks

The Fundamental Theorem of Calculus Part 2 states that if $F(x)$ is an _________ of $f(x)$, then $\int_{a}^{b} f(x) dx = F(b) - F(a)$, where $a$ and $b$ are the _________ of _________.

(Answers: antiderivative, limits, integration)

💡 Part C: Critical Thinking

Explain, in your own words, why the Fundamental Theorem of Calculus Part 2 is so useful in calculus. Provide an example.