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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)

### Use a double integral to find the area of the region

Use a double integral to find the area of the region. Above the cone z=squareroot(x^2 + y^2) and below the sphere x^2 + y^2 + z^2 = 1

### Polar coordinate integrals

See attached page for integrals Evaluate the given integrals by changing to polar coordinates.

### 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

### Reverse order of integration

Evaluate the integral by reversing the order of integration (see attachment for integral)

### 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

### Area between polar curves

See attached Compute the area of the region that lies inside the polar curve...

### 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.

### Derivatives and integrals of vector functions

See attachment for problem

### Evaluate the integral: Int [(1+t^2)i + (-4t^4)j - (t^2 - 1)k]

Evaluate the integral: Int [(1+t^2)i + (-4t^4)j - (t^2 - 1)k]

### 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

### Integration Volume Problem

See attached problem. Integrate from 0 to 3, (pi*x/100)*(sin(pi*x^2/9))dx.

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 integral for fractions

Please show detailed steps of how to evaluate the following integrals. Thank you. (i) (ii) Thank you.

### 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

### Integral - Integrate e^(t^2) dt [See attached integral problem.]

[See attached integral problem.] Integrate e^(t^2) dt

### Integration Function Square Roots

Integrate: x / (sq. root (1 + 2x)) dx from 0 to 4

### Integration - cosxsin(sinx)dxfrom 0 to Pi/2

Integrate: cosxsin(sinx)dx from 0 to Pi/2

### Integration

Integrate sinx / (1+cos^2(X))

### Integration Evaluations

Integrate [(sinx +sinxtan^2(X)) / sec^2(X) ]dx evaluate from 0 to Pi/3