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

=

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     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.

Posted Date: 9/13/2012 7:34:33 AM | Location : United States

Ask an Expert

Related Discussions:- Integration, Assignment Help, Ask Question on Integration, Get Answer, Expert's Help, Integration Discussions

Write discussion on Integration
Your posts are moderated

Write your message here..

Related Questions

Dy/dx, how do you differentiate sinx/ex? how do you differentiate sinx/ex?

Formula to estimate distance around circle table, If Lisa wants to know the... If Lisa wants to know the distance around her circular table, that has a diameter of 42 in, which formula will she use? The circumference or distance around a circle is π times

Canada australia eire spain, Before independence, Bangladesh was called Cey... Before independence, Bangladesh was called Ceylon East Pakistan Bhutan Bangalore Which of the following countries does not have a monarch as head of state? Canada Australia Eire

Area under curve, Write a program to find the area under the curve y = f(x)... Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b

What is the value of m+n, Every point (x,y) on the curve y=log2 3x is trans... Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

INTEGRAL CALCULUS, INTEGRATION OF 1/(1+3 SIN^2 x) INTEGRATION OF 1/(1+3 SIN^2 x)

#rounding off, I am the least two digit number which round off to 100? I am the least two digit number which round off to 100?

Evaluate the measure of the larger angle, Two angles are complementary. The... Two angles are complementary. The calculate of one angle is four times the measure of the other. Evaluate the measure of the larger angle. a. 36° b. 72° c. 144° d. 18°

Perform algebraic operation , Perform each of the following algebraic expr... Perform each of the following algebraic expression as instruction says;- I.Multiply 5x+6m+4y by5 II.Divide 4ax+6ay-10az by 2a

Customary units of length, Eileen needs 9 feet of fabric to make a skirt. I... Eileen needs 9 feet of fabric to make a skirt. If Eileen has 18 feet of fabric how many skirts can she make?