Geometric construction of numerical integration, Engineering Mathematics

Assignment Help:

The integral

1725_Geometric construction.png

has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on bases Δt =T/N , showing that

1378_Geometric construction1.png

Observe that this function is periodic. For a given choice of f and T construct a table to show by how much the discrete version of the integral differs from the true value. Does inclusion of only half the areas of the end rectangles make much difference? Note that you have included N+1 points in your sum. What happens if you have only N points, i.e., if you do not include one of the end rectangles. A geometric construction may assist.


Related Discussions:- Geometric construction of numerical integration

Beta gamma functions, integral dx/root of sinx using beta and gamma functio...

integral dx/root of sinx using beta and gamma functions

Explain how conduction takes place in conductors, With the help of energy b...

With the help of energy bands explain how conduction takes place in conductors. On the basis of energy band materials are categorized as conductor is given below: Conducto

Monthly salary of the clerk , The price indices for the monthly basis salar...

The price indices for the monthly basis salary of a clerk in years 1992 and 1994 based on year 1990 are 128 and 135. The monthly salary of the clerk in the year 1994 is RM810.

Produce a discrete time series, Produce a discrete time series y(t i ) by s...

Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus

Christian maturity level , A researcher is interested in comparing the Chri...

A researcher is interested in comparing the Christian maturity level of students who volunteer for community service versus those who do not. The researcher suppose that those who

Temperature function, If a temperature function is given in the x,y plane b...

If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 decimal places, of the corresponding temperature function T1(u,v) at the point (u,v) =

Mechanical advantage, MA for pulling a 1500 gram cart up a 20 degree plane ...

MA for pulling a 1500 gram cart up a 20 degree plane up a 1 meter ramp using a wheel and axel. Wheel diameter is 8 cm

Database management system, outline the three schema database architecture ...

outline the three schema database architecture clearly explaining each level and how the user view the information

Power of iota, if the power of iota is even then what is the logic to break...

if the power of iota is even then what is the logic to break the power of iota

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