The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus (FTC) often makes it easy to evaluate definite integrals, at least when an antiderivative can be found. It also helps us find a total change in a function by integrating a rate of change (derivative). The units of an integral of f(x)dx are the units of f(x) times the units of x, which helps interpret its meaning in real life applications. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

Calculus problems and solutions

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions): https://www.youtube.com/watch?v=oS-gvIoJf60

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UFYjlnGUenE

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

#FundamentalTheorem #FTC #DefiniteIntegral

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(0:00) Geometric integration
(2:41) Integral as a limit of a Riemann sum
(8:00) Fundamental Theorem of Calculus to compute the definite integral
(10:31) FTC integral evaluation and real life interpretations
(21:05) Trig integral evaluation and real life interpretations
(27:27) Find coffee temperature when given its rate of change
(32:30) Graphical interpretation on a derivative graph (of symbolic expressions)
(36:47) Velocity graphs categorization

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