Integrals

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Algebra: Evaluating Definite Integrals

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

Integrals Evaluated Over Sin

Evaluate the integral sin^-1x dx 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

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

Trigonometric Integration by Substitution

∫ sin θ/√(R^2 + z^2 - 2Rz cos θ) dθ See attached file for full problem description. keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple

Integration by Substitution

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

Continuously Differentiable Functions with Compact Support

Let f : [0,∞)-->R be continuously differentiable with compact support in [0,∞); and 0<a<b<∞. Prove that: ∞ ∫ [f(bx)-f(ax)]/x dx = -f(0) ln (b/a) 0

Continuous Functions, Sequence of Functions and Convergence

Please see the attached file for the fully formatted problem.

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

Numerical Integration of a Differential Equation: Explicit Euler, Implicit and Analytic

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Creating a Function Command in SQL

Evaluate the integral of several trigonometric functions.

Evaluating Trigonometric Integrals

Please see the attached file for the fully formatted problems.

Determine integral 16 (2x + 1)^7 dx

16 (2x + 1)^7 dx

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

Evaluate the indefinite integral of the transcendental function.

Evaluate the indefinite integral of the transcendental function. See attached file for full problem description. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, cal

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.

Indefinite Integrals

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

Disk or Shell Method : Volume of a Solid Revolution

Please see the attached file for the fully formatted problems.

Shell Method: Volumes of Solids of Revolution

Shell Method to Evaluate the Integral. See attached file for full problem description.

Derivatives, logarithmic differentiation, and integration of transcendental functions.

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple Find the derivative of y with respect to the appropriate variable. 1) 2) 3) 4) 5) 6) Use logarithmic differentiation to find the derivative

Trigonometric Integral Descriptions

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

Improper Integrals Question

Please see the attached file for the fully formatted problems. Explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges. integral (1 / ((x-3)^3/2)) dx Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.