Second Fundamental Theorem of Calculus (Part 2)
Second Fundamental Theorem of calculus also called the Fundamental Theorem of Calculus Part 2 states that, if f(x) is continuous on the closed interval [a, b] and F(x) is the antiderivative of f(x), then
∫ab f(x) dx = F(b) – F(a)
The second fundamental theorem is also known as the evaluation theorem. This theorem says that the solution of ∫ab f(x) dx is equal to the difference between the value of the F at the upper limit b and the value of F at the lower limit a.
Remark on Second Fundamental Theorem of Calculus
Various remarks for Second Fundamental Theorem are,
- In ∫ab f(x) dx expression, the function f(x) must be well defined and continuous in [a, b] interval.
- It is a very helpful theorem as it provides a method of estimating the definite integral without finding the sum’s limit.
- In estimating the definite integral, the main operation is finding a function whose derivative is the equation to integrate and this process will strengthen the differentiation and integration relationship.
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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