Integrals

What is Integral Class 11?

Integral is the inverse operation of the differentiation, in differentiation we find the slope of the given curve at any point where as in integrals we find the area between the curve and the axis respectively.

What is the Integral of 2?

Integration is the reverse process of the differentiation. We know that integration of constant c is cx + d. So, ∫ 2 dx = 2x + c

What is integral of 3x?

Integration of x is x²/2. So, integration of ∫3x.dx = 3/2x² + c.

What are Types of Integrals?

There are two types of Integrals, that are,

• Indefinite Integrals
• Definite Integrals

What is the Integral of Sin x?

Integral of Sin x is Cos x, i.e.

• ∫ sin x dx = cos x + c

What is the Integral of Cos x?

Integral of Cos x is -Sin x, i.e.

• ∫ cos x dx = -sin x + c

What is the integral of 1?

The integral of the constant function f(x) = 1 with respect to x is simply x plus a constant of integration. Mathematically, it is represented as: ∫1dx = x+C where C is the constant of integration.

What is the integral of 0?

The integral of the constant function f(x) = 0 with respect to x is 0 plus a constant of integration. Mathematically, it is represented as: ∫0dx = C where C is the constant of integration.

How to calculate integrals?

Integrals can be calculated using various techniques, including:

• Analytical Methods: Such as integration by parts, substitution, partial fractions, and trigonometric substitutions.
• Numerical Methods: Such as the trapezoidal rule, Simpson’s rule, and numerical integration techniques.
• Software Tools: Many mathematical software packages and programming languages have built-in functions for calculating integrals numerically or symbolically.

Is integrals and integration same?

“Integrals” and “integration” are closely related terms but refer to slightly different concepts. “Integration” is the process of finding the integral of a function, while “integrals” refer to the results of that process. An integral can be either indefinite (representing a family of functions) or definite (representing a specific numerical value).

What is the symbol of integral?

The symbol used to denote integration is ∫ (long S). It represents the integral of a function with respect to a variable. For example, ∫f(x) dx represents the integral of the function f(x) with respect to the variable x. If limits of integration are specified, they are written as subscripts and superscripts, such as ∫_a^b ​f(x) dx, where a and b are the lower and upper limits, respectively.

Integrals: An integral in mathematics is a continuous analog of a sum that is used to determine areas, volumes, and their generalizations. Performing integration is the process of computing an integral and is one of the two basic concepts of calculus.

Integral in Calculus is the branch of Mathematics that deals with finding integrals of the given functions. The branch of calculus that deals with integral is called Integral Calculus.

In this article, we will learn about the Integral definition, types, formulas, properties, examples solved problems, etc.