Fundamental Theorems of Integral Calculus
The integral represents the area under the curve. There are two fundamental theorems of integral calculus:
- First Fundamental Theorem of Integral Calculus
- Second Fundamental Theorem of Integral Calculus
First Fundamental Theorem of Integral Calculus
The first fundamental theorem of integral calculus states that if P(x) = ∫ f(x) dx is a continuous function on the interval [a, b], then P'(x) = f(x) for all x ∈ [a, b].
Second Fundamental Theorem of Integral Calculus
The second fundamental theorem of integral calculus states that if f(x) is a continuous function on the interval [a, b] and p(x) is the antiderivative of f(x), then [Tex]\int\limits_a^b [/Tex]f(x) dx = p(b) – p(a) where the integral is called as a definite integral and a and b are called as lower and upper limits of the integral respectively.
Integral Calculus
Integral Calculus is the branch of calculus that deals with topics related to integration. Integrals are major components of calculus and are very useful in solving various problems based on real life. Some of such problems are the Basel problem, the problem of squaring the circle, the Gaussian integral, etc. Integral Calculus is directly related to differential calculus.
This article is a brief introduction to Integral Calculus, including topics such as fundamental theorems of integral calculus, types of integral, and integral calculus formulas, definite and indefinite integrals with their properties, applications of integral calculus, and their examples.
Table of Content
- What is Integral Calculus?
- Fundamental Theorems of Integral Calculus
- Integral Definition
- Types of Integrals
- Definite Integrals
- Definite Integral Formula
- Properties of Definite Integrals
- Indefinite Integrals
- Properties of Indefinite Integrals
- Improper Integrals
- Multiple Integrals
- Integral Calculus Formulas
- Methods to Find Integrals
- Applications of Integral Calculus
- Differential vs Integral Calculus
- Integral Calculus Examples
- Practice Problems on Integral Calculus
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