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

Calculus, The law of cosines can only be applied to acute triangles. Is thi...

The law of cosines can only be applied to acute triangles. Is this true or false?

Subtraction - vector arithmetic, Subtraction - Vector arithmetic Compu...

Subtraction - Vector arithmetic Computationally, subtraction is very similar.  Given the vectors a → = (a 1 , a 2 , a 3 ) and b → = (b 1 , b 2 , b 3 ) the difference of the t

What''s my balance, I should have an account balance for $50.96. You took o...

I should have an account balance for $50.96. You took out $50.96 for a product on 6/18 which was NOT downloaded or delivered as it not available in the time frame I needed it. I am

Find the length of chord ab, If PA and PB are tangents to a circle from an ...

If PA and PB are tangents to a circle from an outside point P, such that PA=10cm and ∠APB=60 o . Find the length of chord AB.

Shares and dividend, what all can be the table contents for my maths projec...

what all can be the table contents for my maths project on shares and dividend

Fraction, Ask question #Minimum 100 words accepted

Ask question #Minimum 100 words accepted

#change of ratio, #in a picnic the ratio of boys to girls is 3:4. when 6 bo...

#in a picnic the ratio of boys to girls is 3:4. when 6 boys joined the group the ratio became even. how many boys were there before? how many children were there before? how many b

Fractions, how do you convert in a quicker way?

how do you convert in a quicker way?

Evaluate the area of the shaded region, Using the example provided, Evaluat...

Using the example provided, Evaluate the area of the shaded region in terms of π. a. 264 - 18π b. 264 - 36π c. 264 - 12π d. 18π- 264 b. The area of the shaded r

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