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

Evaluate distance traveled by train, Evaluate distance traveled by train: ...

Evaluate distance traveled by train: A plane flying at 525 miles per hour completes a trip in 2 hours less than another plane flying at 350 miles per hour.  What is the distan

Example of partial fraction decomposition, Example of Partial Fraction Deco...

Example of Partial Fraction Decomposition Evaluate the following integral. ∫ (3x+11 / x 2 -x-6) (dx) Solution: The 1 st step is to factor the denominator so far as

Coefficients of the equation, If coefficients of the equation ax 2 + bx + ...

If coefficients of the equation ax 2 + bx + c = 0, a ¹ 0 are real and roots of the equation are non-real complex and  a + c (A) 4a + c > 2b (B) 4a + c Please give t

How to subtract fractions with the same denominators, Q. How to Subtract fr...

Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul

What is the probability that the product xy less than 9, A number x is ...

A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected  from  the  numbers  1,4,9. What  is  the  probability that  the product xy of the two

Initial value problem, An IVP or Initial Value Problem is a differential eq...

An IVP or Initial Value Problem is a differential equation with an appropriate number of initial conditions. Illustration 3 : The subsequent is an IVP. 4x 2 y'' + 12y' +

Decmals, just want to go over it

just want to go over it

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