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Double Integrals : Transformation

Please see the attached file for the fully formatted problems. calculate the integarl of (3x + 4) over the region bounded by the lines y =x, y = x-2, y =-2x and y = 3 - 2x; Use: x = 1/3(u+ v), y = 1/3(v - 2u)

Indefinite integral

See attached Find the indefinite integral using each specified method. Then write a brief statement explaining which method you prefer. x (square root of 4-x) dx (a) By parts, letting dv = square root of 4-x (b) By parts, letting u = square root of 4-x

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

Double integral and area

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

Differential equation

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 help

I need help integrating the following problems. I have attached them in a file. Please show step by step solutions.

Evaluate the integral.

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

Maximum and minimum

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

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

Integration help

I am having problem integrating this problem. I am not coming up with the right solutions. Please help me solve this and show all steps. Thanks


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

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 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


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


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


Find the mass of the tetrahedron with vertices (0,0,0), (0,1,0), (3,0,0), and (0,1,4) with density f(x,y)= xy using iterated integral the instructor said that the integral needs to be divided into 2 integrals