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

Distribution of sample distribution or sampling means , Distribution of Sam...

Distribution of Sample distribution or Sampling means A sample of size n is taken from the parent population and mean of the sample is estimated. It is repeated for a number o

What kinds classroom activities help children to learn maths, What kinds of...

What kinds of classroom activities can you think of for helping children to make groups of 5 and 10? Once they have enough practice with such activities, children can be helped

Differential equation to determine initial value problem, Solve the subsequ...

Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t

Euler equations, Euler Equations - Series Solutions to Differential Equ...

Euler Equations - Series Solutions to Differential Equations In this section we require to look for solutions to, ax 2 y′′ + bxy′ + cy = 0 around x0  = 0. These ki

Mathematical methods of economic analysis, I need answers for these 10 exam...

I need answers for these 10 exam questions: 1.Input-output (Leontief) model: main assumptions and construction. Definition of productivity. Necessary condition of productivity of i

Give the example of exponents, Give the example of Exponents? When a nu...

Give the example of Exponents? When a number is multiplied several times, it is easier to write it as an exponent. For example, four multiplied to itself three times, is writte

Unit Rates, I need help on how to do real word problm with unit rates.

I need help on how to do real word problm with unit rates.

Learning, my math skills are keeping me from getting my ged need help in al...

my math skills are keeping me from getting my ged need help in all areas

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