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

Elementary row operations, Anne, Betty and Carol went to their local produc...

Anne, Betty and Carol went to their local produce store to buy some fruit. Anne bought one pound of apples and two pounds of bananas and paid $2.11. Betty bought two pounds of appl

Adding & subtracting i guess, Jack and his mother paid $11.50 for tickets t...

Jack and his mother paid $11.50 for tickets to the movies, and adults tickets cost $4.50 more than a child ticket what was the cost of each ticket?

Positive skewness-measure of central tendency, Positive Skewness - It ...

Positive Skewness - It is the tendency of a described frequency curve leaning towards the left. In a positively skewed distribution, the long tail extended to the right. In

Determine the domain of the function, Determine or find out the domain of t...

Determine or find out the domain of the subsequent function. r → (t) = {cos t, ln (4- t) , √(t+1)} Solution The first component is described for all t's. The second com

Basic computation formulas of differentiation, Basic "computation" formulas...

Basic "computation" formulas : Next, let's take a quick look at some basic "computation" formulas that will let us to actually compute some derivatives. Formulas 1)   If f

Formulas of summation notation, Formulas Now there are a couple of nice...

Formulas Now there are a couple of nice formulas which we will get useful in a couple of sections. Consider that these formulas are only true if starting at i = 1. You can, obv

Pre calculus , use the point to generate a cosine function that models the ...

use the point to generate a cosine function that models the sound wave. Name the amplitude Name the period Name the phase shift name the vertical shift Write the equation for the

Vectors and sclara, find the angel between the vectors 4i-2j+k and 2i-4j on...

find the angel between the vectors 4i-2j+k and 2i-4j online answer

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