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Integrals

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?

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

Lebesgue Integration and Measure Theory

(R,B,&#955;) denote the real line with Lebesgue measure defined on the Borel subsets of R. And 1&#8804;p<&#8734; 1. Show that the sequence fn = n &#967;[1/n, 2/n] (&#967; is a step function) has property that if &#948;>0, then it is uniformly convergent on the complement of the set [0,&#948;]. However, show that there does

Solid of Revolution

Concern the region bounded by: y=x^2 y=1 and the y axis find the volume of the solid obtained by rotating the region around the y-axis

Integrals

Evaluate the integral sec^4 theta tan^4 theta dtheta with a lower limit of 0 and an upper limit of pi/4

Definite Integrals

Evaluate the integral: lnx / x^2 dx with lower limit of 1 and an upper limit of 2.

Integrals

Evaluate the integral sin^-1x dx keywords: integration, integrates, integrals, integrating, double, triple, multiple

Solid of Revolution

Find the volume of the solid obtained by rotating the region bounded by the curves x = y - y^2 and x = 0 about the y=axis. Use the disk or washer method.

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

Trigonometric Integration by Substitution

&#8747; sin &#952;/&#8730;(R^2 + z^2 - 2Rz cos &#952;) d&#952; See attached file for full problem description. keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple

Integration by Substitution

&#8730;2h &#8747; r/(&#8730;(h^2 + r^2 - &#8730; hr) 0 Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Volume of Solids of Revolution

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 region bounded above by y=cosx, below by y=sinx and on the left by the y-axis For the following probl

Mean value of a function

Find the mean value of the function: f(x) = 1 + cos (x) in the range -pi/2 <= x <= pi/2 keywords: integration, integrates, integrals, integrating, double, triple, multiple

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

Trigonometric Integrals

See attached file for full problem description. Only circled questions to be done. 1. Integration 0 to pi/2 cos^2x dx 2. Integrate Sec^2(2c-1)dx 3. Integrate tan^2x dx

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