Integration, Mathematics

Assignment Help:

Integration

We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by   F'(x)  Often, we may know the rate of change,  F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative,   F'(x).  Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.

Let f(x) = F'(x)  The integral of f(x) is mathematically expressed as

451_integration.png

= F(x) + c

The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol   2116_integration1.png  is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:

If  d/dx {F(x)} = f(x) then we can also write that  d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.


Related Discussions:- Integration

Idk, Are you suppose to divide the 1 or subtract

Are you suppose to divide the 1 or subtract

matlab, how to solve simplex method using matlab

how to solve simplex method using matlab?

Quick help for exam preparation, can you help me with entrance exam for uni...

can you help me with entrance exam for university ? i really need help so quick

Prove that its inclination theta to the horizontal, Two stations due south ...

Two stations due south of a tower, which leans towards north are at distances 'a' and 'b' from its foot. If α and β be the elevations of the top of the tower from the situation, Pr

Discrete-time signals as energy or power signals, Classify the following di...

Classify the following discrete-time signals as energy or power signals. If the signal is of energy type, find its energy. Otherwise, find the average power of the signal. X 1

Method to determine solution is absolute value, Method to determine solutio...

Method to determine solution is absolute minimum/maximum value Let's spend a little time discussing some methods for determining if our solution is in fact the absolute minimum

Regression, regression line drawn as Y=C+1075x, when x was 2, and y was 239...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Boeing Company and Ingredient Branding Strategies, . The Boeing Company ma...

. The Boeing Company makes a number of different types of aircraft for the commercial airline industry, e.g., the 727, 747, 757, 767, and 777 jet models. Is there any way for Boei

Laplace transform, what is the Laplace transform of e^9(-t)^a)

what is the Laplace transform of e^9(-t)^a)

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd