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

Objectives of ones tens and more, Objectives After studying this unit, ...

Objectives After studying this unit, you should be able to 1.  evolve and use alternative activities to clarify the learner's conceptual 2.  understanding of ones/tens/hu

Definition of the laplace transform, Definition Assume that f(t) is a ...

Definition Assume that f(t) is a piecewise continuous function. The Laplace transform of f(t) is denoted L{ f (t )} and defined by, There is an optional notation for L

Basics of vectors - calculus, Vectors - The Basics Let us start this s...

Vectors - The Basics Let us start this section off with a quick discussion on what is the use of vector.  Vectors are utilized to present quantities that have both a magnitude

Fractions, What fraction could you add to 4/7 to get a sum greater than 1

What fraction could you add to 4/7 to get a sum greater than 1

Statistical inference, Statistical inference This is the process of dra...

Statistical inference This is the process of drawing conclusions about attributes of a population based upon information contained in a sample or taken from the population.

Semi-infinite slab solution in fourier number, Consider the temperature dis...

Consider the temperature distribution in a 1D flat plate, insulated at x = L and exposed to convective heat transfer at x = 0. On the axes below, sketch what the distribution looks

Point, what will be the activity of the above said title

what will be the activity of the above said title

Partial Differential Equation, Determine the minimum capacity C of a Capaci...

Determine the minimum capacity C of a Capacitor given that: C =(ax/(x-a))+(xy/(y-b))+(yb/(b-y)) given that "a" and "b" are fixed values and "x" and "y" vary independently such th

Find the maximum expected holdings, Problem: A person has 3 units of mo...

Problem: A person has 3 units of money available for investment in a business opportunity that matures in 1 year. The opportunity is risky in that the return is either double o

Math, is this free for LIFE that means forever never ever going to pay

is this free for LIFE that means forever never ever going to pay

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