Share
Explore BrainMass

Integrals

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 -∞ and ∞. I1 = ∫ df / [α2 + (2πf)2] I2 = ∫ sinc2(τf) df I3 = ∫ df / [α2 + (2πf)2]2 I4 = ∫ sinc4(τf) df

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

Evaluate the given line integral and the given surface integral.

Do the following: (1) Evaluate Int(P(x, y) dx + Q(x, y) dy) over the curve C, where P(x, y) = y^2, Q(x, y) = 3x, and C is the portion of the graph of the function y = 3x^2 from (-1, 3) to (2, 12). Here, "Int" stands for integral. (2) Use the Divergence Theorem to evaluate the surface integral Int(F*n ds) over the surface S

Area and volume using multiple integrals

1 Find the area of the part of the surface 2z = x^2 that lies directly above the triangle in the xy-plane with the vertices at (0,0),(1,0) and (1,1). 2 Find the volume of the region in the first octant that is bounded by the hyperbolic cylinders xy = 1, xy = 9, xz = 4, yz = 1, and yz = 16. Use the transformation u = xy, v =

Stokes' Theorem : Curls and Surface Integrals

Let F = (2x, 2y, 2x + 2z). Use Stokes' theorem to evaluate the integral of F around the curve consisting of the straight lines joining the points (1,0,1), (0,1,0) and (0,0,1). In particular, compute the unit normal vector and the curl of F as well as the value of the integral:

Integration Word Problems : Rate of change

Suppose that a tank initially contains 2000 gal of water and the rate of change of its volume after the tank drains for t min is '(t)=(0.5)t)-30 (in gallons per minute). How much water does the tank contain after it has been draining for 25 minutes? keywords: integration, integrates, integrals, integrating, double, triple, m

Volume of a solid

The region R is bounded by the graphs of x-2y = 3 and x=y^2. Set up (but not evaluate) the integral that gives the volume of the solid obtained by rotating R around the line x=-1.

Surface Integral of a Paraboloid of Revolution

Let S be the closed surface of the paraboloid of revolution z = ±(4 − x2 − y2 ) where −2 x, y +2. Evaluate the following surface integral directly and then by using the divergence theorem; where R is the position vector to a point on the surface and is the outward pointing normal at that point. See att

Taylor Polynomials and Partial Sums of Series

1 Write the Taylor polynomial with center zero and degree 4 for the function f(x) = e^-x 2 Determine the values of p for which the series ∞ Σ 1/(2p)ⁿ n=1 3 Calculate the sum of the first ten terms of the series, then estimate the error

Integrals

Antidifferentiation ∫(e^x -6) dx

Finding the Volume of a Solid of Revolution

Problem: The region R is bounded by the graphs of x - 2y = 3 and x = y2. Find the integral that gives the volume of the solid obtained by rotating R around the line x = -1. I'm having a hard time setting up the integral, I think that I have the concept for finding the area of a 2d object using an integral but can't figure out

Finding Integrals (8 Problems)

(See attached file for full problem description with proper symbols) --- Answers and working for Integration questions: 1.Integrate the following functions with respect to . (i) sin(5 - 4) (ii) cos(3 - 2) 2. Integrate the following functions with respect to x. (i) 4e-3x (ii) (

Applications of Integrals : Velocity and Acceleration

Newton discovered that the falling acceleration of all objects in a vacuum, regardless of their sizes and weights, is the same. A raindrop falls down to earth with the same acceleration as a big metal ball drops from the edge of a building. He came up with the value of 9.8 meters per square second (s2) for the falling accelerati

Integration, limits, and curves

Note: x is used as a letter only not as a multiply sign 1. Find the volume of the solid generated by revolving the region enclosed by y= x^(1/2), y=0, x=4 about the line x=6. 2. Find the arc length of the graph of the function y = x^(3/2) - 1 over the interval [0,4] 3. Integrate ∫ [(Pi / 2) / 0] x cos x dx

Cartesian Coordinates, Convergence and Divergence

1. Find the equation of the tangent line in Cartesian coordinates of the curve given in polor coordinates by r = 3 - 2 cos Ø, at Ø= (π / 3) 2.Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so. a) ∑[∞/n=1] (3/ 2^n)

Integrals : Finding Work Done

A 100 ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building? keywords: integration, integrates, integrals, integrating, double, triple, multiple