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
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Using: d tan^-1 (x/y)=(y dx - x dy)/(x^2 + y^2), and ½ d ln(x^2 + y^2)=(x dx + y dy)/(x^2 + y^2) find integrating factors for, and solve, the following equation: (2x^(2)y + 2y^3 - x) (dy/dx) + y=0
Find the Laplace Transform of the function F(t) = (1 - e^(-at))/a. Prove by the method of contour integration that F(t) is itself the Laplace Transform of the function arrived at.
Laplace Transform Application of Complex Inversion Integral Formula (Bromwich's Integral Formula) Problem:- Find the Laplace Transform of the function F(t) = (1 - e^(
See word file for problems regarding the ladder method of integration by parts
Show that (7x/x^2 + 5) + (4/3x+15) - (5/6x-24) = (45x^3-15x^2-825x-35)/((6x^2+30)(x^2+x-20)) then use that information to determine S=integral S(45x^3-15x^2-825x-35)/((6x^2+30)(x^2+x-20)) dx.
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
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
Questions on integration, see attachment.
Use the integral test to determine the convergence or divergence of the series: En=1 2 / (3n + 5)
Integral x-1, divided by x to the 3rd + x squared to dx. x-1 ----- X to the 3rd + X to the 2nd ( all dx)
For problem #1, its the integral from o to infinity (the symbol for infinity for that problem was cut off)
I'm taking a DE calculus class and I'm having problems figuring out the logic in solving some of the problems. The given integral is improper because both the interval of integration is unbounded and the integrand is unbounded near zero. Investigate its convergence by expressing it a sum of two intergrands-one from 0 to 1 an
Evaluate the double integral Transform the double integral of (i) using plane polar coordinates Show that the 3 x 3 determinant See attached file:
Please see the attached file for the fully formatted problems. Evaluate the following integrals. S (4x^3 -2x - (2/x^3) dx S (1/2x^1/2) dx 1-->0 S ln x dx