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Integrals

Consumer and Producer Surplus

Problem and example are attached Consumer and Producer Surplus: Find the consumer and producer surplus for the case below: Demand: P1(x) = 1000 - 0.4x62 Supply: P2(x) = 42x.

Triple integral

See attached page Evaluate the triple integral. Triple integral xydV over E where E is the solid tetrahedron with vertices (0, 0, 0), (0, 1, 0), (1, 1, 0), and (0, 1, 1)

Differential equations critical points

Please help on these problems section 5.4 # 2,4,8,12,28,33 Thanks attach is the reference Verify that the pair s(t), y(t) is a solution to the given system... Find the critical point for the given system... Determine the integral curves for the given system.... Solve the phase plane equation...

Integration Blank Spaces

I need help integrating the following problems. I have attached them in a file. Please show step by step solutions. 1. 2. 3. Note: Plug in answer from question 2 into the blank space in question 3 and integrate question 3

Region of integration

Sketch the region of integration and change the order of integration for the attached problems.

Maximum and minimum of a function

Find the maximum and minimum values of: f(x1, x2) = int(1/(1+t^4), t = x1..x2) over the region determined by (x1)^2 * (x2)^2 = 1 (attached is a .jpg version of the function)

Complex Integration

Let be the unit circle, followed in the positive direction. Evaluate the integral. Please show all steps to the solution.

Integrals and Curl Oriented Upward

Let S be the part of the plane z = 2x + y + 5 inside the cylinder x^2 + y^2 = 1 with the normal oriented upwards, and let F := xi - zj - yk. see attached file for problem. Thanks you

Integral

See attached evaluate the integral

Integration by Parts and Motion in a Particle

A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis. (b) Suppose that its acceleration at time t is a=100(1-t)e^(-1). Show that the particle never moves beyond a c

Integration by Parts: Area and Volume

The figure shows the region bounded by the x-axis and the graph of. Use Formulas (42) and (43). Which are derived by integration by parts? To find (a) the area of this region; (b) the volume obtained by revolving this region around the y-axis. Formula (42) Formula (43). See the attached files.

Integration of the Weibull distribution

I am trying to integrate the attached function ( a version of Weibull distribution). I have the solution in Maple -- I think. But I cannot prove it. Tried Integration by parts but still missing something. Please Integrate with respect to y. If it is not clear from the pdf the function is basically : a/b * y ^ (a-1) * e^(-(y

Evaluate the Natural Log Integrals

Please see attachment for full description. Please show detailed steps of how to evaluate the following integrals. (1) [e^x - e^(-x)] / [e^x + e^(-x)]dx (2) 1/[x^(2/3)* (1+ x^(1/3))]dx (3) 1/[1 + sqrt(2x)]dx

Evaluate indefinite integrals

Please see attachment. Show detailed steps of how to evaluate the following integrals 1. (x +1)e^(x^2 + 2x)dx 2. (tanx)^4 * (secx)^2dx

Integral for area Bounded by Two Functions

The problem reads: 1)Plot the following functions on the same coordinate system with the given domain and range. y = x^4 - 2x^2 and y = 2x^2 -4 <= x <= 4 -2 <= y <= 10 2)I am then to set up the definite integral that gives the area of the region bounded by the graphs of the functions. I had no trouble plotting th

Integral Bounded by Two Functions

The problem reads: 1)Plot the following functions on the same coordinate system with the given domain and range. y = x^4 - 2x^2 and y = 2x^2 -4 <= x <= 4 -2 <= y <= 10 2)I am then to set up the definite integral that gives the area of the region bounded by the graphs of the functions. I had no trouble plotting th