Share
Explore BrainMass

Integrals

Surface Integrals

Find the surface integral (double integral over S) E dot dS, where S is the cylinder, x^2 + y^2 = 4, z is greater than or equal to 2 and less than or equal to 5, and the vector field F is F(x, y, z) = (0, 0, z^2)

Vector Fields and Surface Integrals

Find the flux of the vector field F(x, y, z) = (y, 0, z2) out of the unit sphere S. In other words, find the surface integral ∫∫S (y, 0, z2) * dS, where the sphere S is oriented by the outward normal. Let S be the cylinder x2 + y2 = 1, 0 ≤ z ≤ 6. Find ∫∫S (x4 + 2x2y2 + y4)2 dS.

Calculus: Evaluating an Integral

Let C be the curve represented by the equations x = 2 t , y = 3 t^(2). Evaluate the integral (0 <= t <= 1) / l (x - y)ds . l / C

Cantor Sets

1. Show that the Cantor function c: [0, 1] → [0, 1] is continuous. To do this, I know I need to use the fact that c is monotone, but I'm having difficulty from there. 2. Compute ∫c, where c is considered to be an element of L+(R). (let c(x) =0 for x not in [0, 1]) Here, c is the Cantor Function and L+(R) consists

Contours and the Cauchy Integral Formula

Let C be the boundary of the square of side length 4, centered at the origin, with sides parallel to the coordinate axes, and traversed counterclockwise. Evaluate each of the attached integrals.

Linear Operators, Inner Products and Adjoints

We are studying an inner product spaces. See attached file for full problem description. Let V be a C-space of all complex valued polynomials with an inner product.... (i) Let p be a polynomial and let Mp: V-> V be a linear operator that is given by Mp (q) :=p&#8901;q. Show that operator Mp has an adjoint and find it. (i

Approximating an integral

Approximate the integral by: a) first applying Simpson's Rule b) then applying the trapezoidal rule See attached file for full problem description.

Convergence and infinite series

1.) Find the interval of convergence of the series &#931; (for n=0 to &#8734;) (4x-3)^(3n)/8^n and, within this interval, the sum of the series as a function of x. 2.) Determine all values for which the series &#931; (for n=1 to &#8734;) (2^n(sin^n(x))/n^2 converges. 3.) Find the interval of convergence of the series &#931

Show that the two iterated Riemann integrals of the given function of two real variables are unequal to each other, and that the absolute value of the function is not Lebesgue integrable.

Let f be the following function with domain C = [0, 1] X [0, 1] (in two-dimensional Cartesian space): f(x, y) = 0 on the line segments x = 0, y = 0, and x = y f(x, y) = -1/(x^2) if 0 < y < x <= 1 f(x, y) = 1/(y^2) if 0 < x < y <= 1 Compute each iterated Riemann integral of f on C (by integrating first over x and then

Sequences and Improper Integrals

1.) Show that the functions f1(x)=5^x, f2(x)=5^(x-3), ans f3(x)=5^x + 3^x all grow at the same rate as x approaches infinity. 2.) Determine whether each integral converges or diverges. a.) integral from 0 to 2 of (dx)/(4 - x^2) b.) integral from 0 to infinity of (5 + cosx) e^(-x)dx c.) integral from 0 to in

Integration by Substituton

I am having problems understanding how to solve linear equations. For example, dy/dt = -4y + 3e^-t Can you solve this step-by-step so that maybe I can understand how to do it myself?

Explicit Rule & Recursive Rule & Integrals & Exponential Growth

1.) For the arithmetic sequence {-10,-2,6,14,}, find: a.) a recursive rule for the nth term b.) an explicit rule for the nth term 2.) For the geometric sequence {512,256,128,64,...}, find: a.) a recursive rule for the nth term b.) an explicit rule for the nth term 3.) Determine whether each of the follo

Vector Fields, Fundamental Theorem of Line Integrals

1. Find the curl of the vector field F at the indicated point: 2. Evaluate the following line integral using the Fundamental theorem of line Integrals: 3. Use Green's Theorem to calculate the work done by the force F in moving a particle around the closed path C: 4. Find the area of the surface over the part of the

Solid of Revolution

Find the volume of the solid bounded by x = 0, y = 0, z = 0 and x + 2y + 3z = 6 by triple integration. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Integrals : Rayleigh's Energy Theorem ( Parseval's Theorem )

Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -&#8734; and &#8734;. I1 = &#8747; df / [&#945;2 + (2&#960;f)2] I2 = &#8747; sinc2(&#964;f) df I3 = &#8747; df / [&#945;2 + (2&#960;f)2]2 I4 = &#8747; sinc4(&#964;f) df

Center of Mass of a Lamina; Polar Coordinates and Jacobians

Find the mass and center of mass of the lamina bounded by the graphs of the given equation and of the specified density. Use polar coordinates to evaluate where R is the region enclosed by . Suppose the transformation T is defined by and . Find the Jacobian, , of T. Please see the attached file for t

Lebesgue Integration

For what values of a in R (real numbers) is the function (1+x^2)^a in L^2 NOTE: let L^2 be like in Lebesgue integration where the set of all measurable functions that are square-integrable forms a Hilbert space, the so-called L2 space. keywords: integration, integrates, integrals, integrating, double, triple, multiple, r

Volume of Solids of Revolution

Please help with the following problems. Please provide step by step calculations and diagrams. For the following problem, sketch the region and then find the volume of the solid where the base is the given region and which has the property that each cross-section perpendicular to the x-axis is a semicircle. 1) the regio

Determining where a function is continuous, Epsilon-Delta Continuity Problem

Determine where the function f(x) = x + [|x^2|] - [|x|] is continuous I don't understand how to work this problem. Can someone show and explain how to solve this problem in detail? I've asked for help on this problem before but I still don't understand it. The function is continuous everywhere but 0. I don't understan

Definite Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Indefinite Integrals

Please see the attached file for the fully formatted problems. keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving keywords: integration, integrates, integrals, integrating, double, triple, multiple

Definite Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple, areas keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Find the indefinite integrals and check the results by differentiation.

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Indefinite Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Set up the definite integral that gives the area of the region.

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Trigonometric Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

Integrals

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving