C is an arbitrary constant. It doesn't matter whether you use "c" or "25/4+ c" it still represents some arbitrary constant.sgstudent said:Homework Statement
If i integrate (2x+5) using the simplest rule, i get x2+5x+c, however if i use the linear function method, i would get (2x+5)^2/4 +c so simplifying it i get (4x^2+20x+25)/4 +c=x^2+5x+25/4+c. So does it mean when i use the two different methods my constant,c is different?
Homework Equations
linear integration rule
The Attempt at a Solution
So does it mean when i use the two different methods my constant,c is different?
sgstudent said:Homework Statement
If i integrate (2x+5) using the simplest rule, i get x2+5x+c, however if i use the linear function method, i would get (2x+5)^2/4 +c so simplifying it i get (4x^2+20x+25)/4 +c=x^2+5x+25/4+c. So does it mean when i use the two different methods my constant,c is different?
Homework Equations
linear integration rule
The Attempt at a Solution
So does it mean when i use the two different methods my constant,c is different?
Integration of linear functions is the process of finding the area under a linear function on a given interval. It is the inverse operation of differentiation, and it involves finding the antiderivative of the function.
The purpose of integrating linear functions is to solve problems that involve finding the total amount or accumulated value of a changing quantity over a given time period. It is also used to find the average value of a function and to calculate displacement, velocity, and acceleration.
To integrate a linear function, you need to first find the antiderivative of the function. This involves using integration rules and techniques, such as the power rule, substitution, and integration by parts. Once you have found the antiderivative, you can then evaluate the integral at the given limits to find the area under the curve.
Definite integration of linear functions involves finding the area under the curve between two given limits. It results in a specific numerical value. Indefinite integration, on the other hand, involves finding the general form of the antiderivative of the function and does not involve evaluating at specific limits.
Integration of linear functions is used in a variety of fields, such as physics, engineering, economics, and finance. It is used to calculate quantities such as displacement, velocity, acceleration, work, and profit. It is also used in the process of curve fitting, which is used to model and predict real-life data.