First Fundamental Theorem of Calculus (Part 1)
The First Fundamental Theorem of Calculus also called “Fundamental Theorem Part 1” states that if f(x) is a continuous function on the closed interval [a, b] and the function F(x) is defined by
F(x) = ∫ax f(t) dt
Then,
F'(x) = f(x) over [a, b]
where, F'(x) is derivative of F(x)
Fundamental Theorem of Calculus | Part 1, Part 2
Fundamental Theorem of Calculus is the basic theorem that is widely used for defining a relation between integrating a function of differentiating a function. The fundamental theorem of calculus is widely useful for solving various differential and integral problems and making the solution easy for students.
This is widely used in the fields of physics, engineering, medicine, economics, biology, space exploration, statistics, pharmacology, and many more.
Before learning about the fundamental theorem of calculus let’s first learn about calculus and others. In this article, we will learn about calculus, area function, the fundamental theorem of calculus, and others.
Table of Content
- What is Calculus?
- Differential Calculus
- Integral Calculus
- Area Function
- Fundamental Theorem of Calculus
- First Fundamental Theorem of Calculus (Part 1)
- First Fundamental Theorem of Calculus Proof
- Finding Derivative using Fundamental Theorem of Calculus
- Second Fundamental Theorem of Calculus (Part 2)
- Remark on Second Fundamental Theorem of Calculus
- Second Fundamental Theorem of Calculus Proof
- Fundamental Theorem of Calculus Examples
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