Name: Fundamental Theorem of Calculus, Part 2, Definite Integrals, Basic Proof - Calculus
Uploaded: 2025-10-22T12:00:00+00:00
Duration: 1 min 5 s
Description: The Second Fundamental Theorem of Calculus states that for a continuous function f on the interval [a, b], the definite integral from a to b is equal to the difference between the value of any antider

3 days ago

Health & Science Education proof of the fundamental theorem of calculus part 2 proof of the fundamental theorem of calculus- part 2 fundamental theorem of calculus part 2 fundamental theorem of calculus part 1 proof of the fundamental theorem of calculus proof of fundamental theorem of calculus second part of the fundamental theorem of calculus fundamental theorem of calculus (part2) the fundamental theorem of calculus

The Second Fundamental Theorem of Calculus states that for a continuous function f on the interval [a, b], the definite integral from a to b is equal to the difference between the value of any antiderivative F at b and the value of F at a. Its formula is: ∫baf(x)dx = F(b) − F(a), where F'(x) = f(x). This theorem provides a powerful method for evaluating definite integrals by finding an antiderivative and evaluating it at the integral's limits.

💡Here's a breakdown of the theorem:
• The Setup: You start with a function f(x) that is continuous on the interval [a, b].
• The Antiderivative: You find an antiderivative of f(x), which is any function F(x) such that its derivative, F'(x), is equal to f(x).
• The Calculation: The theorem says that the definite integral, which represents the area under the curve of f(x) from a to b, can be calculated by taking the antiderivative F(x), evaluating it at the upper limit b (F(b)), and then subtracting the value of the antiderivative evaluated at the lower limit a (F(a)).

💡Why is it important?
• Simplifies Calculation: It provides a direct method to calculate definite integrals, replacing the more complex process of breaking the area into infinite tiny rectangles (numerical integration).
• Connects Integration and Differentiation: It establishes a fundamental link between the process of integration and differentiation by showing that integrating a function's derivative gives you back the original function (up to a constant difference).
• Applications: It is widely used in various fields to find total changes by integrating a rate of change. For example, if f(x) is a velocity function, the integral of f(x) from a to b gives the total displacement over that time interval.

💡Worksheets are provided in PDF format to further improve your understanding:
• Questions Worksheet: https://drive.google.com/file/d/1nyZAxMFIv3phTs8a9uQiZ7WKvrQ4fBKt/view?usp=drive_link
• Answers: https://drive.google.com/file/d/16wbbNzLH-O0LGu6SEvM5Nq9gNQlpoR-H/view?usp=drive_link

💡Chapters:
00:00 Fundamental theorem of calculus, part 2

🔔Don’t forget to Like, Share & Subscribe for more easy-to-follow Calculus tutorials.

🔔Subscribe: https://rumble.com/user/drofeng
_______________________
⏩Playlist Link: https://rumble.com/playlists/Ptm8YeEDb_g
_______________________
💥 Follow us on Social Media 💥
🎵TikTok: https://www.tiktok.com/@drofeng?lang=en
𝕏: https://x.com/DrOfEng
🥊: https://youtube.com/@drofeng