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

Green''s funtion., show that the green''s function for x"=0,x(1)=0,x''(0)+x...

show that the green''s function for x"=0,x(1)=0,x''(0)+x''(1)=0 is G(t,s)=1-s

Five shirts and one tie cost $20 what price of one shirt, Three shirts and ...

Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt? Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part

What could the dimensions of the floor be in terms of x, Harold is tiling a...

Harold is tiling a rectangular kitchen floor with an area that is expressed as x 2 + 6x + 5. What could the dimensions of the floor be in terms of x? Because area of a rectang

Describe order of operations with example, Describe Order of Operations wit...

Describe Order of Operations with example? The order of operations is a set of rules that describe the order in which math operations are done. Try doing this math problem:

Prove any prime number is irrational, 1. Show that there do not exist integ...

1. Show that there do not exist integers x and y for which 110x + 315y = 12. 2. If a and b are odd integers, prove that a 2 +b 2 is divisible by 2 but is NOT divisible by 4. H

rules for solving linear in-equations - linear algebra, Explain what are t...

Explain what are the Rules for solving linear in-equations?

Find out the linear approximation, Find out the linear approximation for a...

Find out the linear approximation for at x =8 .  Utilizes the linear approximation to approximate the value of  and Solution Since it is just the tangent line there

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