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    Representation of the Dirac Delta Function

    Please see the attached file for the fully formatted problems. Show that is a representation of the Dirac S-function. Discussion: Let and let f(x) be a function which is piecewise continuous on [?a, a], in particular, (Dirac delta function) one must show that One way of doing this is to follow the approach u

    Integrating Periodic Functions

    Please see the attached file for the fully formatted problems. Suppose that f(x + 2pi) = f(x) is an integrable functionof period 2pi. Show that S f(x) dx 2pi + a ---> a = S f(x) dx 2pi ----> 0 where a is any real number.

    Integration By Trigonometric Substitution: Solving Trickier Problems?

    Hello! I'm having trouble using Trigonometric Substitution to find the anti-derivative of non-simple integrands. For details on my situation, please consult my missive, which I've included as an attachment in MS Word '95 (WordPad compatible) and Adobe PDF (ver 3+) files. (The files contain identical information; if you can re

    Curve Sketching, Integration, Stationary Points and Asymptotes

    Please see the attachment for the full question. I require full, detailed, step by step workings for all sections of this problem Coursework 2 Question 2 a) For the curve with the equation y = x^3 + 3x^2 - 2 i) Find the position and nature of any stationary points. ii) Make up tables of signs for y, y' and y''. Us

    Multivariable Calculus : Iterated Integral

    ( f ^n_r means that n is on the top of the f and r is on the bottom) Evaluate the iterated integral: f ^(pi/2)_0 f ^(pi/2)_0 cos x sin y dy dx f: is the integral symbol

    Multivariable Calculus: Triple Integral - Cylindrical Coordinates

    Question: Solve by triple integration in cylindrical coordinates. Assume that each solid has unit density unless another density function is specified: Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2.

    Multivariable Calculus : Triple Integral

    Compute the value of the triple integral   _T f(x, y, z) dV: f(x, y, z) = xyz; T lies below the surface z = 1 - x^2 and above the rectangle -1*x*1, 0*y*2 in the xy-plane. : is the integral symbol

    Multivariable Calculus : Double Integral - Polar Coordinates

    (  ^n_r means that n is on the top of the  and r is on the bottom) Evaluate the given integral by first converting to polar coordinates:  ^1_0  ^(square root of 1 - x^2)_0 (1/(square root of 4 - x^2 - y^2)) dy dx : is the integral symbol

    Multivariable Calculus : Integral Explanation

    Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. (  ^n_r means that n is on the top of the  and r is on the bottom) Sketch the region of integration, reverse the order of integration, and evaluate the resulting integral:  ^1_0  ^1_y

    Volume Using Cylindrical Shells

    The region bounded by the curve and the lines and is revolved around the x-axis to form a solid S. The volume of S by the method of washers is given by the integral . Find the volume using the method of cylindrical shells. Please show the complete solution (particularly how to find the cross-sectional area), including al

    Integral Solution Evaluation

    Please see the attached file for full problem description. Can somebody help me to evaluate the following integral,

    Calc II/Setting up integral to calculate volume of rotation

    a) Take the region bounded by y = cos x and y = 1 - x for 0 ≤ x ≤ and rotate about the line x = . Set up the integral which calculates the volume of rotation (using one variable only). b) Complete the integration without using integral formulas or calculator estimates. (Please show work on this so that I can see

    Differential Equation

    Given dy/dx= -xy/(ln y), where y>0 find the general solution of the differential equation What solution satisfies the condition that y=e^2 when x=0... express in y=f(x) Why is x=2 not in the domain found from that?

    Integrals and Continuity Calculus

    20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) - f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain

    Arc Length

    Evaluate the integral in the attached file "Arc Length.doc" for arc length (L). The intent is to solve for a numerical answer and the values for a, b, and t are all constant.

    Transformation to Evaluate the Double Integral

    Please see the attached file for full problem description. --- Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x+y)sin(x-2y). over the square region with vertices at (0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables). Solution. Letting

    Use a transformation to evaluate the double integral

    Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x-y)sin(x+2y) over the square region with vertices at O(0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables)

    Working between the integral

    Can anyone show me the working between the integral in the enclosed file & the answer of A = 4/3 First let's sketch the graph for 0≤t≤2п: Ok, so one loop is the half of this, i.e. 0≤t≤п: Now we have: where x=f(t) and y=g(t). Then we have: or: A=4/3

    Double Integral

    Can anyone please show me how to solve these double integrals, with a step by step approach. I know the answer is 63 - but Ive tried so many times & I don't know where I'm going wrong. upper limits are 1&y=2 x+4y^2 dydx + lower limits are -2&y=-x upper limits are 4 & y=2 x+4y^2 dydx lower limits ar

    Double Integral over a Square Region

    Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x-y)sin(x+2y) over the square region with vertices at (0,0) (1,-2) (3,-1) & (2,1) (My notes from class-uses substitution, change of variables) I have let u=(2x-y) & v=(x+2y) using substitution (change of variables)

    Population model

    In some populations, the amount of births is directly proportional to the population at any given point in time and the amount of deaths is directly proportional to the square of the population at any given point in time. 1. Write an equation that models the change in a population that fits the above description. Make sure t