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

Explain set intersection, Q. Explain Set Intersection? Ans. Set I...

Q. Explain Set Intersection? Ans. Set Intersection Suppose your school needs to know which students are taking both art and business this year. If A is the set of studen

Determine coefficient of traction, Problem 1 Work through TALPAC 10 Bas...

Problem 1 Work through TALPAC 10 Basics (refer to attached handout). Answer the set of questions at the end of tutorial module. Problem 2 Referring to both the haul cyc

Math, a business is owned by three people.the first owns 1/12 of the busine...

a business is owned by three people.the first owns 1/12 of the business and the second owns 1/6 of the business. what fractional part of the business is owned by the third person

What was the dow at the end of the day after the 2% drop, The Dow Jones Ind...

The Dow Jones Industrial Average fell 2% presently. The Dow began the day at 8,800. What was the Dow at the end of the day after the 2% drop? The Dow lost 2%, so it is worth 9

Volume of solids, find the volume of a rectangular based right pyramid with...

find the volume of a rectangular based right pyramid with its base 18 cm by 24 cm and the slanted edge 39 cm

Sums and differences of cubes and other odd powers, Sums and Differences of...

Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =

Find the perimeter of triangle, The length of the sides of a triangle are 2...

The length of the sides of a triangle are 2x + y/2 , 5 x/3 + y + 1/2  and 2/3 x  + 2y + 5/2. If the triangle is equilateral. Find its perimeter. A ns: 2x + y/2 = 4x + y

Equation: 4x^4+9x^4=64 , If 4x^4+9x^4=64 then the maximum value of x^2+y^2 ...

If 4x^4+9x^4=64 then the maximum value of x^2+y^2 is solution) From the eq. finding the value of x^2 and putting it in x^2 + y^2.we get 2nd eq. differentiating that and putting

Methods for doing integral, There are really three various methods for doin...

There are really three various methods for doing such integral. Method 1: This method uses a trig formula as,  ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c

Find out the next number 320, Find out the next number in the subsequent pa...

Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.

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