0
Where you refer to a particular integral I will assume you mean a definite integral. To illustrate why there is no constant of integration in the result of a definite integral let me take a simple example. Consider the definite integral of 1 from 0 to 1. The antiderivative of this function is x + C, where C is the so-called constant of integration.
Now to evaluate the definite integral we calculate the difference between the value of the antiderivative at the upper limit of integration and the value of it at the lower limit of integration:
(1 + C) - (0 + C) = 1
The C's cancel out. Furthermore, they will cancel out no matter what the either antiderivatives happen to be or what the limits of integration happen to be.
Still curious? Ask our experts.
Chat with our AI personalities
Ezra
Fran
SteveAdd your answer:
Earn +20 pts
How do you find integration ofcos sinx?
It seems that you can't express that integral in terms of a finite number of commonly used functions. In the Wolfram Alpha site (input: "integral cos sin x"), you can find the first few terms of an infinite series expansion.
Why does you put plus c after integration?
When you find an indefinite integral of a function (ie, the integral of a function without integration limits) you are actually finding the antiderivative of that function. In other words, you are finding the function whose derivative is the function 'inside' the integral sign. Recall that the derivative of a constant is zero. The point here is that you add the 'c' to acknowledge the fact that when the derivative of the result of your integration effort is taken to get the original function it could, or would, have been followed by some unknown constant value that disappeared upon differentiation. That constant is denoted by the 'c'.
What is Integration by substitution?
It means that you substitute one expression by another, as a step of the integration. When you do a substitution, you must not forget to also substitute the differential in the integral, for example the "dx" (if the variable integrated is "x"). You can find some examples on how to do this in the Wikipedia article on "integration by substitution".
IN Trapezoidal Rule for Numerical Integration How you can find error?
in trpezoidal rule for numerical integration how you can find error
What is the difference between vertical and horizontal integration?
Horizontal integration is the process of merging similar industries, industries that produce similar products. Vertical integration is the process of buying out suppliers of that particular industry. The main difference is that horizontal integration buys the competing companies while vertical integration aims at the raw material sources necessary to produce that product
