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

Parabola, please i need the answers to x^_7x+10 i want the vertex,axis of s...

please i need the answers to x^_7x+10 i want the vertex,axis of semetery,y intersect and the x intercept

Intrgers, how to evaluate the sums

how to evaluate the sums

Systems of equations revisited, Systems of Equations Revisited We requ...

Systems of Equations Revisited We require doing a quick revisit of systems of equations. Let's establish with a general system of equations. a 11 x 1 + a 12 x 2 +......

More volume problems, More Volume Problems : Under this section we are de...

More Volume Problems : Under this section we are decide to take a look at several more volume problems. Though, the problems we see now will not be solids of revolution while we

Find out if the sets of vectors are parallel or not, Determine or find out ...

Determine or find out if the sets of vectors are parallel or not. (a) a → = (2,-4,1), b = (-6, 12 , -3) (b) a → = (4,10), b = (2,9) Solution (a) These two vectors

Fft algorithm, (a) Using interpolation, give a polynomial f ∈ F 11 [x] of d...

(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which

International marketing, what are challenges and solution of international ...

what are challenges and solution of international marketing

What is the total balance of an account after 18 months, A certain bank pay...

A certain bank pays 3.4% interest per year for a certificate of deposit, or CD. What is the total balance of an account after 18 months along with an initial deposit of $1,250?

How much money does she have left, Mary has $2 in her pocket. She does yard...

Mary has $2 in her pocket. She does yard work for four various neighbors and earns $3 per yard. She then spends $2 on a soda. How much money does she have left? This translates

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