Reduction formulae, Mathematics

Assignment Help:

 

Reduction formulae

Script for Introduction:

First let us know what is meant by reduction formula.

In simple words,

                A formula which expressess(or reduces) the integral of the nth  indexed function in terms of that of n-1th  indexed function is called a Reduction formula.

 

Let us see how reduction formula helps us in solving the problems in different cases:

 

Problem 1:

Solve  Integration of

sin4x dx

Script for this problem:

This problem can be solved by reduction formula for sine which states that,

// print line 1

 

Here we have n=4.

Therefore substituting the value  of n=4 in the given problem,we have,

//print line 2

 

Which is equal to,

//print line 3

 

On expanding  I2 in a similar manner, we can write I4 as,

//print line 4

 

Now, we know that,

//print line5

 

Which is equal to,

//print line 6

 

Here substituting the value of I0 in the equation of I4 ,we have

//print line 7

 

Thus, by reduction formula  the given problem is solved.

 


Related Discussions:- Reduction formulae

Solid Mensuration, The two sides of a triangle are 17cm and 28cm long, and ...

The two sides of a triangle are 17cm and 28cm long, and the length of the median drawn to the third side is equal to 19.5 cm. What is the distance from an endpoint of the median to

Vectors - calculus, Vectors  This is a quite short section. We will b...

Vectors  This is a quite short section. We will be taking a concise look at vectors and a few of their properties. We will require some of this material in the other section a

The achievements from math, i love math..but i am afraid to study it... i m...

i love math..but i am afraid to study it... i mean i ma afraid that it may leave me in clay...what can you suggest me?

Measurement, into how many smaller part is each centimeter divided

into how many smaller part is each centimeter divided

Solving trig equations with calculators, Solving Trig Equations with Calcul...

Solving Trig Equations with Calculators, Part I : The single problem along with the equations we solved out in there is that they pretty much all had solutions which came from a

Solve out the linear equations, Solve out each of the following equations. ...

Solve out each of the following equations.                3( x + 5)= 2 ( -6 - x ) - 2x Solution In the given problems we will explained in detail the first problem and t

Need answer!, what is the basic unit of weight in the metric system?

what is the basic unit of weight in the metric system?

Design an automaton that accepts only even numbers, Design an automaton tha...

Design an automaton that accepts just only even numbers of 0s and even number of 1's. Ans: The needed automata that accepts even number of 0's and even number of 1's is specifi

Constantinople byzance adrienople nicosia, What was the name of Istanbul be...

What was the name of Istanbul before its capture by the Turks? Constantinople Byzance Adrienople Nicosia

Mensuration, A palm tree of heights 25m is broken by storm in such a way th...

A palm tree of heights 25m is broken by storm in such a way that its top touches the ground at a distance of 5m from its root,but is not separated from the tree.Find the height at

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