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

How many times must he mow across the width of the lawn, Allan has been hir...

Allan has been hired to mow the school soccer field that is 180 ft wide through 330 ft long. If his mower mows strips which are 2 feet huge, how many times must he mow across the w

Differentiate inside function in chain rule, Differentiate following. f ...

Differentiate following. f ( x ) = sin (3x 2   + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.

I need help with math, can i get help with math just with fractions i want ...

can i get help with math just with fractions i want to catch up with my class

Introduction to technical mathmatic, 81 miles equal how many inches simplif...

81 miles equal how many inches simplify your answer integer od decimal..

Simultaneous equations with two or more than two variables, Method to solve...

Method to solve Simultaneous Equations with two or more than two variables Method  Above we have seen equations wherein we are required to find the value of the

Mod(z-25i)<15, Mod(Z-25i)   Sol) mod (Z-25i) means Z lies in the circumfer...

Mod(Z-25i)   Sol) mod (Z-25i) means Z lies in the circumference of the circle with (0,25) at its centre and radius less then 15. so difference in the max and min value of arg Z is

Which of the subsequent numbers is equivalent to 12.087, Which of the subse...

Which of the subsequent numbers is equivalent to 12.087? Zeros can be added to the end (right) of the decimal portion of a number without changing the value of the number; 12.

Minimum value of the function, How the property AM>or = GM used to get min...

How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a

Mortgages, compute the monthly payment on a 30 year level payment mortagage...

compute the monthly payment on a 30 year level payment mortagagesasuming an annual mortgages principal of $400000

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