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# Integrals

### Properties of Integrals : Verify an Inequality

Use the properties of integrals to verify the inequality without evaluating the integral: [the integral as 1 goes to 2 of (sqrt(5-x))dx] is greater than or equal to [the integral as 1 goes to 2 of (sqrt(x+1))dx].

### Integrals : Riemann Sum with Diagrams

This question has me going around in circles. I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it. (a)Find an approximation to the integral as 0 goes to 4 of (x^2-3x)dx using a Riemann sum with right endpoints and n=8. (b)Draw a diagram

### Elementary Numerical Analysis

GAUSSIAN NUMERICAL INTEGRATION 1. Consider approximating integrals of the form... in which f(x) has several continuous derivatives on [0, 1] a. Find a formula... which is exact if f(x) is any linear polynomial. b. To find a formula... which is exact for all polynomial of degree &#8804; 3, set up a system of four e

### Elementary Numerical Analysis : Gaussian Numerical Integration

1. Show that if an integration formula of the form In ( f ) = &#8721; wjf(xj) is exact when integrating 1, x, x2, ..., xm, then it is exact for all polynomials of degree &#8804; m. Please see attached for proper format of question.

### Line Integral of Curve which is the Union of Two Line Segments

Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, -1) and the second going from (3, -1) to (6, 0). Compute the line integral. Please see attached.

### Evaluate the integral.

∫x/[x + (x^1/2) -2]

### Improper Integrals; Hyperbolic Functions; Convergence and Divergence etc.

Please assist me with the attached problems, including: Show that the improper integral converges and find its value or show that it diverges ... Please see attachment for complete list of questions.

### Integrals; Exact Value; Volume; Length (30 Problems)

Please assist me with the 30 attached problems, including: - Finding integral - Finding exact value - Finding volume - Finding length.

### Integrals; Sine; Cosine; Bounded Region etc.

Please assist me with the attached problems. Examples: 2. Find each integral 5. Integrate equations using tables 6. Derive the sine squared formula 42. Use substituion to integrate certain powers of sine and cosine 52. Find the area of the region bounded by the graphs etc. (see attachment)

### Arc Length of Curve, Tangent Line, Limits and Solid Revolution

1. Find the volume of the solid generated by revolving the region enclosed by: {see attachment} 2. Find the arc length of the graph of the curve {see attachment} 3 - 7. Integrate attached equations ... 8. Find the limit of the improper integral: {see attachment} 9. Find the arc length of the curve given in parametric

### Find the Mass of a Prism Given a Density Function

Find the mass of the rectangular prism .... with density function ... where m = triple integral of density. Please see the attached file for the fully formatted problem.

### Indented Path : Integral of Branch of Multiple-Valued Function

Show that... by integrating an appropriate branch of the multiple-valued function... over (a) the indented path in Fig. 97, Sec 75; (b) the closed contour in Fig. 99, Sec. 77. See attachment for equations and diagrams.

### Use a Function to Derive a Pair of Integration Functions

Use the attached function to derive the pair of integration functions {see attached for functions and diagram}

### Solving: Improper Integrals

Use residues to evaluate the improper integrals (see the attachment to view the problem).

### Evaluate the Following Integrals (4 Problems)

Evaluate the following integrals: 4 1. ∫ (2x-3)(x+2)dx 2 2 2. ∫ (2x+1)4dx 1 0.001 3. ∫ 50cos50πt dt -0.001 π/2 4. ∫ 5sin(2t-(π/6)dt 0

### Integral

Find the integral of [x/(-x^2+6x+13)^(1/2)]dx

### Find an integral by substitution.

Find the integral of dx/1+(x)^1/2

### Integration by Parts

Integral of (t^2)Ln(t-2)dt

### Polar Coordinates : Evaluating an Improper Integral

A) Using polar coordinates, evaluate the improper integral {see attached} B) Use part A to evaluate the improper integral {see attachment} *Part A is completed, but I need some help with Part B

### Residues and Poles : Value of Integral (Counterclockwise around a Circle)

Fine the value of the integral {see attachment} taken counterclockwise around the circle: (a) |z| = 2 (b) |z + 2| = 3 Please specify the terms that you use if necessary and clearly explain each step of your solution.

### Residues and Poles : Cauchy Integral Formula

Find the value of the integral: {see attachment} taken counterclockwise around the circle (a) |z - 2| = 2 (b) |z| = 4 Please specify the terms that you use if necessary and clearly explain each step of your solution.

### Volume of Solid of Revolution (4 Problems)

52. Find the volume V of the solid with the given information regarding its cross-section: {see attachment for info and diagram) 55. Find the volume of the solid generated when the region {see attachment} on the interval {see attachment} is revolved about a) the x-axis b) the y-axis c) the line y = -2

### Volume of Solid of Revolution : Finding Volumes and Setting up Integrals (15 Problems)

1. Use shells to find the volume of the solid formed by revolving the given region about the y-axis: {see attachment for regions} 2. Set up but do not evaluate an integral using the shaded strips {see attachment} for the volume generated when the given region is revolved about a) the x-axis b) the y-axis c) the line y = -

### Find Areas and Sketch Bounded Regions (Curve)

2. Sketch a vertical or horizontal strip and find the area of the given regions bounded by specified curves: a), b), c) and d) {see attachment!} 3. Sketch the region bounded by and between the given curves and then find the area of each region: a), b), c), d), e) and f) {see attachment!}

### Lowest Common Multiples and Diophantine Equations

Please solve the following problems: 1. Compute the following ... 2. Let Fm be the set of all integral multiples of the integer m. Prove that ... 3. Draw the graphs of the straight lines defined by the following Diophantine equations ... 4. Prove that every integer is uniquely representable as the product of a non-negati

### Green's, Divergence and Stokes theorems Describe in 5-15 lines the links and connections among Green's theorem in all forms, Stokes' theorem and the Divergence theorem. In particular, your answer should address the question: Which theorem is an extension to which other theorem and in what way?

Real Analysis Divergence Theorem Green's theorem stokes' theorem

### Subring R of Integral Domain D is a Subdomain of D

Modern Algebra Ring Theory Subrings Integral Domain

### Green's Theorem and Stokes' Theorem

Using Green's Theorem and Stokes' Theorem respectively, calculate the given line integrals. • Using Green's Theorem calculate the line integral , where along the positively oriented closed curve C which is the boundary of the domain: . Which line integrals you would have to evaluate instead in order to calculate h

### Multiple Integration, Area, Center of Mass, Centroid and Jacobian

1.Given the region R bounded by y=2x+2 , 2y=x and 4. a) Set up a double integral for finding the area of R. b) Set up a double integral to find the volume of the solid above R but below the surface f(x,y) 2+4x. c) Setup a triple integral to find the volume of the solid above R but below the surface f(x,y)=-x^2 +4x. d) Set

### Find the work done by a force on a body along a curve.

Find the work done by a force F with F = (x,y,z) = (sinx, x+y, e^z) which results in the movement of a body along the curve C with parameterization r = (t, t^2, logt)for tE[1,2]. (See attachment for second question)