Undergraduate differentiation of a definite integral

By applying the method of differentiation of a definite integral to show that: (i) There is a second question, but I am unsure of how to solve this, so I would appreciate any guidance so I can attempt the second question myself. Thanks :).

Sixth form Definite Integral of Sin(x) - is it 4 or 0?

Very basic question. What's the definite integral of sin(x) with limits of 0 to 2pi. Is it 0 or 4? If the limits are 0 to pi it is 2; and if the limits are from pi to 2pi, then it is -2. Is the definite integral the sum of the area, in which case the absolute value of -2 is taken, so it adds up to 4, since area is always positive? Or is t...

Double integral in Mathematica - how do I understand the output?

I am trying to compute a definite integral in Mathematica. This is the input I use, where L, D, H, W, k are all constants: Integrate[k*(cos(theta))^2*(L-(D-H*sin(p hi)*tan(theta))) *(W-abs(H*cos(phi)*tan(theta))), {theta, 0, pi/2}, {phi, 0, 2*pi}] and it gives me the output: -(1/480) cos^2 k pi^4 (abs cos H pi^2 tan (-15 D + 15 L + 8 H pi...

Undergraduate Surface integral check

Hi guys For this I get the surface integral is zero, because, parameterizing with spherical polars, you basically do the integral of cos(phi) from 0 to 2pi which is zero. But the website says the answer is 16pi - which I don't agree with. Can anyone confirm which is right?...

Undergraduate Triple integral question

I need help on a triple integral. It is simply the triple integral of 1 (so volume) over the set A in where and . I tried to do it using cylindrical coordinates and got . But my answer is clearly wrong since it's negative. How would I approach this one?...

Undergraduate Convergence of integral

For what values of c does integral from 0 to infinity of f(x) converge, where f(x) = x^c / sqrt(x^2 + x) I really have no idea where to start with this question and would appreciate some help! Thanks a lot...

Undergraduate Paticular integral for vector differential equation

Hi guys, Question is above. I am stuck on part (c). The complementary function has a term of the form A e^(2t), hence for part (c), the particular integral will be te^(2t), where is a column vector (c_1, c_2, c_3). But when I try to solve for c I get something hideous and most likely I am doing it wrong since it can't be that messy. How...

DJCAD Applicants 2013

Hello there! I'm applying to Duncan of Jordanstone this year, for the general course. :) I was there for the academic year 2010/2011, but I switched course. However, that didn't work out because it wasn't the course that was the problem! So I'm trying again. Anyway, I'm just posting this in case anyone else on here is applying for 2013 en...

Sixth form Calculator

I am looking to get a calculator that can do symbolic integration and differentiation. E.g. If I put in the integral of (sin2x) it will give me -0.5cosx What is the best (preferably cheap!) calculator that can do this? Btw I know these are not allowed in UK exams..

Applying for PhD, but Master's degree GPA...sigh.

Hi, I am currently doing a master's degree and applying for PhD. The matter that tackles me is the GPA of the master course. I am applying for the uni that I did undergraduate, so I have a strong supportive supervisor. But I am worried that the requirements for PhD are expected as distinction or merit, but I don't think I can get those. M...

Undergraduate I'm confused (about prime ideals and maximals)...

Quote: Let and let be a prime number. Show that is a prime ideal which is not maximal. (Hint: What is So I've got that is a field is maximal. And 2) is prime is an Integral Domain. Now, is a field, and an Integral Domain by 2). Therefore would be maximal by 1). But that defies the question? What am I getting wrong here? :hmmmm2:...

Sixth Form C3 integration

2 Questions: Now I know I could multiply out brackets and integrate but I'm wondering if I've missed a more straigtforward method. The chapter I'm on is about how to differentiate and integrate functions of the form , but this integral doesn't seem to be in this form. I get the integral as , giving me a final answer of , but according to...

Undergraduate Proof, modular arithmetic, probs & stats

Hey, too many questions. 1.Is the reasoning in the first pic ok? Edit. No it wasn't. 2. Is this correct? 3. How is integral of Mx(t) not negative? 4. Is my venn ok? I can get P(C n D) but then am not so sure what is going on, tried a few things. I should be aiming for the space to be 1 right? 5. What is that symbol about? How can I find t...

Sixth form C4 OCR MEI EXERCISE 8b QUESTION 7 iii)

The question is as follows: Use the results to show that the integral of xsin(5x)sin(3x) dx = (pi-2)/16, to which an upper limit of pi/4 and lower limit of 0. The results from the previous parts are that the integral of xcos(kx) dx is equal to 1/k xsin(kx) + 1/k^2 cos(kx)+c. From what I have worked out from the previous parts, and from wh...

How to shade region under the curve in matplotlib

I want to use matplotlib to illustrate the definite integral between two regions: x_0, and x_1. How can I shade a region under a curve in matplotlib from x=-1, to x=1 given the following plot import numpy as np from matplotlib import pyplot as plt def f(t): return t * t t = np.arange(-4,4,1/40.) plt.plot(t,f(t))...

Undergraduate Partial differentiation chain rule

Hi there, I am given that u = F(x - ct), where F() is ANY function. I have to calculate partial du/dt and partial du/dx [for the adjective eqn.) So i started off with letting s = x - ct So then u = F(s), and partial ds/dt = -c, and partial ds/dx = 1 I think I have to work out partial du/dF, and partial du/ds, so then partial du/dt = [part...

Undergraduate Lagranges multipliers

I have to find the volume of a cube which has a surface area 270 and the second constraint is that one of the sides is 5 times greater than another. I set down the equations as f(x,y,z)=xyz g(x,y,z, (xy+yz+xz)=135 and h(x,y,z, (x-5y)=0 I am having difficulty solving the simultaneous equations. Can I ask if I have the equations set out cor...

Test Shoei GT-AIR - L'intégral voyageur et sportif !

Alors qu'il va arriver chez vos revendeurs préférés, nous avons déjà pu rouler quelques milliers de kilomètres avec le Shoei GT-Air, le nouvel intégral de la marque japonaise. Ce casque, à vocation routière et look sportif, est doté d'un intérieur en...

Is what seems like polymorphism in PHP really polymorphism?

Trying to figure out whether PHP supports features like method overloading, inheritance, and polymorphism, I found out: it does not support method overloading it does support inheritance but I am unsure about polymorphism. I found this Googling the Internet: I should note that in PHP the polymorphism isn't quite the way it should be. I...

Blackhat Cash.. Make 1000$ or more.. The First Working Ebook [2013]

I have the resale Rights of this fantastic ebook http://www.hackforums.net/showthread.php ?tid=3192501 TOS The method has been written for information only I take no responsibility on how you are using this method. You can not resell this ebook You can not give it away You can not exchange it for any other book To buy the book contact me,...

Applying to both Cambridge and Oxford for Postgrad

Hi everyone, I'm a student in a US college, and I'm interested in applying to both Cambridge and Oxford for a taught Master's. I've heard something about people not usually applying to both at the same time. Is that the case for someone like me (international student applying for postgrad degree)?...

Matrix of Differential Operators in Python module Sympy

When applying the Ritz Method to solve a curved beam, the internal energy can be represented as: U=w/2*{c}.T*(integral( r*[g].T*[B].T*[F].T*[B]*[g], -a, a)*{c} where is the transpose. Disregarding the other terms, the [B] matrix is a matrix of differential operators given in the code below. Trying to solve this using Sympy the following...

Sixth form MEI Maths AS level C2 Differentiation Chapter assessment ?

Hi, so I am really stuck on this chapter assessment of differentiation because my class moves too fast as our teacher doesn't have time to fit all the modules in for the exam. I was just wondering if anyone could help me and i would appreciate it so much because i am struggling so much at the moment. 4) A curve has the equation y= 2x^3 -...

Cardiff University Scholarships for Undergraduate Students in UK, 2014

Cardiff University is offering undergraduate scholarships for UK students. The Scholarships are available to undergraduate students beginning their studies in .. [Read Full Scholarship Detail]...

Why is does inheritance order or mapping affect the subscript of the vftable? (for the VSC for C++)

When playing a little bit around with polymorphism, I've tried to do something like the following: class a { virtual void method() { } }; class b { virtual void method() { } }; class c : public a, b { virtual void method() { } virtual void anotherMethod() { } // (1) class d : public c, a, b // (2) { virtual void method() { } }; // C2369...

Independent student finance

Could anyone give me advice on student finance. I am a mature student (over 25yrs old) and have applied for a 3 year undergraduate degree, starting in September 2013. I have read that i will be classed an an independent student. I am currently living at home with my parents but am i right in thinking that their income is not assessed when...

Applying to med school without biology

Hey guys! Anyone here who's applying to med school without biology or sucessfully got accepted into med school without biology? I TOTALLY regretted not taking bio during As level and I think its too late to do a crash course since I'll be applying to med school this year. Out of the 30+ medschools, I can only apply to 8 of them since most...

Undergraduate Integrating Dirac Delta Function (simple question)

I'm just going over this exam question It's pretty straight forward but I'm getting a conflicting answer with the mark scheme (which I think may be an error) The delta function centres at x = 5 so substituting that in you should get f(5) as the delta function 'filters' to f(x) when integrated. However the mark scheme is showing 5.f(5), pu...

Why mechanical engineering?

I am applying to do engineering and am unsure of what field of engineering to apply for. I have noticed on TSR and from application statistics that a lot of people are applying for mechanical engineering. Why is it more popular than other engineering feilds? I was wondering from any current mechanical engineering students or anyone applyi...

MSc Mathematics and Finance, Imperial College

I'm thinking of applying for this course. Does anyone know how difficult will it be to get in? I have a 2:1 undergraduate degree from the University of Manchester in Mathematics with Financial Mathematics, and have had relevant work experience over the last two years (banking and finance related jobs). Also, is it possible to put my secon...

Derivative expression tree java

I am trying to implement a method that returns a new tree expressing the derivative of an expression. I have the orignal expression tree, as well as an exact copy at my disposal. I know I can to this recursively using differentiation rules and base cases for when a node is a constant or a number. But I'm having trouble wrapping my head ar...

Sixth form C4 integration using substitution help

Hi, just wondering if someone could help me with an integration using substitution question (when you are given u=...). I know you work out du/dx and substitute this and u into the integration and cancel out dx, then work it out.. But I can't see how it works on some questions - like this one.. Use the substitution u= 3x - 1 to express in...

Undergraduate Criminology applicants 2013/14

Who else has applied for undergraduate Criminology? I've got Northumbria as my insurance. :)...

Realizarán feria integral dedicada a la mujer

SD. Desde hoy y hasta el 24 de los corrientes se llevará a cabo la primera Feria Integral de la Mujer, en las instalaciones de Galería 360, bajo la organización de Odelis Soto y su empresa Merkaeventos. Esta feria tiene como objetivo principal exponer el desarrollo de la mujer dominicana a fin de impulsar su crecimiento personal y profesi...

Gobierno presenta plan atención a infancia

SD. El presidente Danilo Medina anunció ayer la puesta en marcha del Plan Nacional de Protección y Atención Integral a la Primera Infancia "Quisqueya Empieza Contigo", con el cual el Gobierno apoyará a las familias, asegurándoles atención integral. El mandatario ofreció los detalles del plan al pronunciar un discurso durante una ceremonia...

esata does not see full ntfs drive

Hi all I have a PK5 premium m/b desktop, using esata connections for my two external drives, a 750g and a 1g both WD in Akasa Integral boxes working ok. I can remove them from esata and connect by usb to my laptop ....works fine. Both using win 7 64. I bought a new 2g Wd and fitted it in an another Akasa Integral box. I formatted it ntfs...

Applying to Uni - Need Help!!

Hello. I have a few questions, that if anyone can answer I would be very Grateful! Abit of a read, but i need to get it clear. So I have lived on my own since I was 16 (now 23) and with my partner for the last 5 years. When applying for student loans/grants will this mean anything? I am willing to work part time for money, but I need to k...

Worth applying IOE?

Hi guys, gosh it's been forever since I've been on this forum! I'm applying for my PGCE now and I know it's late! I have reasons and well, from what I can see on GTTR places are still available for maths. I'm finishing off uni so don't have time to do more experience. My question is, do you think it's worth me applying to IOE. Currently h...

Applying for jobs even if you can't do the specified hours?

There's a job I'm interested in applying for but I could only work 2 of the days they're asking. They specify a "Fixed term contract Monday to Friday 1.30-5.30" I could work the Monday and Friday but have college Tuesday-Thursday, I am also available during the weekend. Is it worth even applying for it because of this or is there a chance...

Alternative student loans undergraduate college loans

Bank of North Dakota (BND) Student Loan Services DEAL Loan : Alternative loan for undergraduate students and high school students participating in dual credit programs.. .. need to know about college student how to get out of student loan debt .. An alternative student loan is a credit-based loan made in the student s name, available for...