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

Describe visualize solutions of simultaneous equations, Describe Visualize ...

Describe Visualize Solutions of Simultaneous Equations ? By drawing the graph of each equation in a system of equations, you can see a picture of the system's solutions. Fo

Nonhomogeneous systems, We now require addressing nonhomogeneous systems in...

We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now.  Sin

What was the total cost of her order, Leslie ordered a slice of pizza for $...

Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +

.., rectangles 7cm by 4cm

rectangles 7cm by 4cm

The prerequisites for multiplication, THE PREREQUISITES FOR MULTIPLICATION ...

THE PREREQUISITES FOR MULTIPLICATION : The word 'multiply', used in ordinary language, bears the meaning 'increase enormously For instance, bacteria multiply in favourable conditi

What is unreducing fractions, Q, Did you know that you can unreduce a fract...

Q, Did you know that you can unreduce a fraction? Ans. Remember, you reduce a fraction by dividing the numerator and denominator by the same numbers. Here we divide

Properties of triangle, In triangle ABC, cosecA(sinB.sinC+cosB.sinC) is equ...

In triangle ABC, cosecA(sinB.sinC+cosB.sinC) is equal to..?

Two train leave show many hours will take before trains pass, Two trains le...

Two trains leave two different cities 1,029 miles apart and head directly toward every other on parallel tracks. If one train is traveling at 45 miles per hour and the other at 53

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