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

Find the polynomial g(x), On dividing the polynomial 4x 4 - 5x 3 - 39x 2 ...

On dividing the polynomial 4x 4 - 5x 3 - 39x 2 - 46x - 2 by the polynomial g(x) the quotient is x 2 - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x 2 +

Identify the children strategies to solve maths problems, Here are four pro...

Here are four problems. Four children solved one problem each, as given below. Identify the strategies the children have used while solving them. a) 8 + 6 = 8 + 2 + 4 = 14 b)

The probability that five randomly selected 3-year old snake, The probabili...

The probability that a randomly selected 3-year old garter snake will live to be 4 years old is .54 (assume results are independent).  What is the probability that five randomly se

Write a procedure to obtain the inverse of a matrix, Write a procedure to o...

Write a procedure to obtain the inverse of an n by n matrix usingGaussian elimination. (You cannot use A - 1 or any of the built-in packages like 'MatrixInverse'.) Output any a

Bisection method and the newton method, 1. Write two m-files, one for the b...

1. Write two m-files, one for the bisection method and another for Newton's method. 2. Using both the Bisection method and the Newton method answer the following: Include th

1 application of complex analysis in THERMODYNAMICS, Hi, this is EBADULLA ...

Hi, this is EBADULLA its about math assignment. 1 application of complex analysis used in thermodynamics. . what all uses are there in that... plz let mee know this answer.

Arclength surprise - mathematics, Suppose a unit circle, and any arc S on t...

Suppose a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is provided, the area between S and the x-axis plus the covered area between S and

Permutation, explain the basics of permutation

explain the basics of permutation

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