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

Operation research, i have assignment in operatuion research can you help m...

i have assignment in operatuion research can you help me

Exercise to think about this aspect of children- maths, Doing the following...

Doing the following exercise will give you and opportunity to think about this aspect of children. E1) List some illustrations of exploration by four or five-year-olds that you

General solution to a differential equation, The general solution to a diff...

The general solution to a differential equation is the most common form which the solution can take and does not take any initial conditions in account. Illustration 5: y(t) =

Algebraic expression, i dont understand what my teacher disccussing thats w...

i dont understand what my teacher disccussing thats why i want to learn for this lesson. i want to ask'' what is the variables?

Ratio and proportion, the sides of triangleare inthe ratio 2;3;4 if the per...

the sides of triangleare inthe ratio 2;3;4 if the perimeter is 72 cm. find its side.

Examining a related problem, how to explain this strategy? how to do this s...

how to explain this strategy? how to do this strategy in solving a problem? can you give some example on how to solve this kind of strategy.

Sums, what is 10 times 10 pls

what is 10 times 10 pls

Find ways in which prizes are distributed between student, Find out the num...

Find out the number of ways in which 5 prizes can be distributed among 5 students such that  (a)   Each student may get a prize. (b)  There is no restriction to the number o

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