### Evaluate the integral

The following expression describes the total electric current to pass in the circuit please see attached

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The following expression describes the total electric current to pass in the circuit please see attached

There is integral domain with exactly six elements. Disprove or Prove

Develop a program (M-File) called 'integrate' that will perform a first-order numerical approximation, yi(t), of the running integral with respect to time of an array of experimental data y(t). The M-File must also perform another first order approximation, yi2(t), of the first integral resulting in a double integration of the

I've included the problem as a JPEG . Thank you You own a plot of riverfront property which is pictured in the figure. Your property runs along the x-axis from x=0 to x=100 and is bounded by the lines x=0, x=100 and the River Sine. 1. What is the equation of the River Sine? 2. What is the area of the plot? 3. You have $6

Why did the Alberti Cipher disk have numbers on it? Describe how the disk was used. What made it secure? What was the impact of this disk on cryptology? How does enciphering and deciphering differ on the Enigma? What weakness in the Enigma did the Poles use to break Enigma ciphers?

Please see the attached file for the fully formatted problems. Problem statement: What really makes Laplace transforms work for differential equations is the relationship between the transform of a function and the transform of the derivative of that function. Therefore, the formula you will prove below is key to all that

Int sqrt{1+x^2}/x dx

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

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?

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

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

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)

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

Laplace Transform Application of Complex Inversion Integral Formula (Bromwich's Integral Formula) Problem:- Find the Laplace Transform of the function F(t) = (1 - e^(

Please see the attached file for the fully formatted problems. Partial fraction decomposition is a technique used to convert a fraction with a polynomial numerator and a polynomial denominator into the sum of two or more simpler fractions. It eases integration by reducing it to the sum of integrals, each of which will most l

1. The shaded region R, is bounded by the graph of y = x^2 and the line y = 4. a) Find the area of R. b) Find the volume of the solid generated by revolving R about the x-axis. c) There exists a number k, k>4, such that when R is revolved about the line y = k, the resulting solid has the same volume as the solid in par

See attachment

Integrate the following: y = (x - x^2)/(x^(1/6))

Please see the attached file for the fully formatted problem. Integrate:

Use an iterated integral to find the area of the region: y = 1 /sq root (x - 1)

Please see the attached file for the fully formatted problem. Use the indicated change of variables to evaluate the double integral: SR S 60xy dA x = 1/2(u + v) y = -1/2(u - v)

Find the indefinite integral (3-x)/sq root of 9-x^2 dx(dx would be in the numerator). I tried to split this problem apart. First part was: The integral of 3/sq root of 9-x^2 dx and found 3 arcsin x/3 + C, then Second part was: The integral of -x/sq root of 9-x^2 dx and found -3/4 -x + C. I then put them back together to ge

Note: If you have already answered this exact question please do not answer it again. I would like an answer from a different T.A. Thanks Say abs = absolute value. Suppose that the function f:[a,b]->R is Lipschitz; that is , there is a number c such that: abs(f(u) - f(v)) <= (c)abs(u-v) for all u and v in [a,b]. Let P

Apply Green's Theorem to evaluate the integral over C of 2(x^2+y^2)dx + (x+y)^2 dy, where C is the boundary of the triangle with vertices (1,1), (2,2) and (1,3) oriented in the counterclockwise direction. Also check the result by direct integration. Please show detailed working so I can follow the steps of the working.

Find the indefinite integrals (anti-derivatives):

Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

Please see the attached file for the fully formatted problems. Sketch the curve r = 5 - 3cos(theta) and set up double integral for bounded area in the third quadrant.

Evaluate the following indefinite integral. int[(x^a)sqrt(r+tx^(a+1))]dx, (t not=0, a not=-1). (See attachment)

1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2) 2) Find the volume of the solid bounded above and below by the cone (z^2) = (x^2) + (y^2), and the side by y=0 and y= square root(4-(x^2)-(z^2))

Please see the attached file for the fully formatted problem. Construct the quickest method to calculate the Laplace Integral. I = S e^(-x^2) dx infinity --> infinity