### Integral evaluation

Please see the attached file for full problem description.

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Please see the attached file for full problem description.

See attached word file.

Show that there are exactly four distinct sets of integers which satisfy the attached equations:

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

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.

Can you show me the solution to this integral? See attached file for full problem description.

Can you please show all the working to solve the attached 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

Can anyone show me the working between the integral in the enclosed file & the answer of A = 4/3

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

Please see the attached file for full problem description.

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

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

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].