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# Integrals

### Integration Problems

-2 1. Evaluate &#8747; (e3x - 4 / ex) dx -3 2. The mean value of a continuous function over a given range is defined as the integral of a function divided by the range. b

### Integrals : For what values of p does the integral converge or diverge? What is the value of the integral when it converges?

For what values of p does the integral converge or diverge? What is the value of the integral when it converges? &#8747;0--> e x^p ln x dx Please explain your answer.

### Heat transfer and Heat Equations

3-3. Use the methods of vector calculus to derive the general heat conduction equation (Hint: Apply the first law to a volume V with surface S. and use the Gauss divergence theorem to Convert the surface integral of heat flow across S to a volume integral over V.) The cylindrical and spherical coordinate systems are examples o

### Use Trapezoidal Rule, Midpoint and Simpson's Rule to Evaluate 9 Integrals

(See attached file for full problem description)

### Integration : &#8747;(2&#952;³-7&#952;²+7&#952;)/(2&#952;-5) d&#952;

Please evaluate the following integral using basic formulas. Rewrite the integral to match it to a standard formula, and then solve the integral. Please show each step in the problem. Thank you. &#8747;(2&#952;³-7&#952;²+7&#952;)/(2&#952;-5) d&#952;

### Integration Using a Trigonometric Formula : &#8747;&#8730;(1-sin²&#952;)d&#952;

Please evaluate the following integral using basic formulas. Rewrite the integral to match it to a standard formula, and then solve the integral. Then evaluate the answer for the values &#960;/2&#8804;x&#8804;pi Please show each step in the problem. Thank you. &#8747;&#8730;(1-sin²&#952;)d&#952;

### Integration by Trigonometric Substitution

Please evaluate the following integral using basic formulas. Rewrite the integral to match it to a standard formula, and then solve the integral. Please show each step in the problem. Thank you. &#8747;dr/r&#8730;(r²-9)

### Integration Using Formulas : &#8747;2dx/x&#8730;(1-4ln²x)

Please evaluate the following integral using basic formulas. Rewrite the integral to match it to a standard formula, and then solve the integral. Please show each step in the problem. Thank you. &#8747;2dx/x&#8730;(1-4ln²x) integrate

### Viscous Fluid Flow : Viscous Drag on the Walls of a Pipe

For laminar flow in the entrance of to a pipe, as shown in figure, the entrance is uniform u=U0, and the flow downstream is parabolic in profileu(r)=C(r0^2-r^2). Using integrla relations, show that the viscous drag exerted on the pipe walls between 0 and x is... Prescribed text book: White, FM, , Viscous Fluid Flow, 2nd Editi

### Integration problems

Can you please provide a detailed explanation of how to evaluate these questions? (See attached file for full problem description)

### Simpson's Rule

Question 1: What is the exact value of &#8747; 0-->2 x^3 + 3x^2 dx ? Question 2: Find SIMP(n) for n = 2, 4, 100. What is noticeable? ---

### Integration using left, right, trapezoid, and midpoint rules

(See attached file for full problem description) Definite integrals 1. Show geometrically why int sqrt (2-x^2) dx = pi/4 + 1/2 2. Approximate int sqrt (2-x^2) dx for n = 5 using the left, right, trapezoid, and midpoint rules. Compute the error in each case using the answer to question 1 to compare the errors

### To solve several definite and indefinite integrals.

Please see the attachment for the questions. Please solve each problem step by step giving solutions please. SHOW every step getting to the answer. Show substitutions, etc. DO NOT SKIP STEPS PLEASE! Look below for attachments. Adult student asking for help and I learn by the examples you solve. I learn different than ot

### Solve

Solve. Show all the steps. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). (see equation in attachment)

### Integrate

Solve. Show all the steps. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). (see equation in attachment)

### Integration by parts

In this problem I am asked to use integration by parts utilizing the formula: &#8747;udv = uv - &#8747;vdu Please show the values of u, dv, du, and v and each of the steps to achieve the solution. This problem may involve more than one sequence in integrating by parts. Thank you. &#8747;4xsec²2xdx

### Integration by parts

In this problem I am asked to use integration by parts utilizing the formula: &#8747;udv = uv - &#8747;vdu Please show the values of u, dv, du, and v and the steps to achieve the solution. Then show the final value after substitution of the limits. Thank you. &#8747;x³lnxdx 1&#8804;x&#8804;e

### Surface area of revolving curve

Using the formula for the surface area of a revolving curve about the x-axis: S=&#8747;2&#960;y&#8730;(1 + (dy/dx)²)dx throughout a,b Find the area of the surface generated by revolving the curve about the x axis within the given boundaries y=&#8730;(x + 1) 1&#8804;x&#8804;5 Please be detailed, showing the compl

### How Corporations Issue Securities : Interest Rate, Issue Cost and Company Expense, Private Placements and Public Issues

You need to choose between making a public offering and arranging a private placement. In each case the issue involves \$10 million face value of 10-year debt. You have the following data for each: A public issue: The interest rate on the debt would be 8.5 percent, and the debt would be issued at face value. The underwriti

### Changing the Order of Integration and Finding the Volume

1. Using the integral &#8747;-1-->1 &#8747;x^2-->1 &#8747;0-->1-y dz dy dx a) Sketch the region of integration. Write the integral as an equivalent iterated integral in the order: b) dy dz dx c) dx dz dy d) dz dx dy 2. Find the volume of a wedge cut from the cylinder x^2 +y^2 =1 by planes z=-y and z=0. Please show me t

### Inverse Trigonometric Functions, and Derivatives

7.5 Inverse trigonometric functions Find the exact value of the expression. 1) sin^-1 (SQRT3 / 2) 2) arctan(-1) 3) tan^-1 (SQRT 3) 4) cos^-1 (-1) 5) csc^-1 (2) 6) arcsin(-1/ (SQRT 2) 7) sec^-1 (SQRT 2) 8) arccos(cos 2pi) 9) tan^-1 (tan 3pi/4) 10) cos(arcsin ½) 11) sin(2 tan^-1 SQRT 2) 12) cos(tan^-1 (2) + tan

### Trigonometric Integrals and Integrate by Substitution

Evaluate the integral 1) ∫ (sin^3 (x)) (cos^2 (x)) dx 2) ∫ ( sin^4 (x)) (cos^5 (x)) dx 3) ∫ ( sin^6 (x)) (cos^3 (x)) dx 4) ∫ ( sin^3 (mx)) dx 5) ∫ (from 0 to pi/2 on top) (cos^2 (theta)) dtheta 6) ∫ (from 0 to pi/2 on top) (sin^2 (2theta)) dtheta 7) ∫ (from 0 to pi on top) (sin^4 (3t)) dt 8) ∫ (from 0

### Integrate by Substitution and Integrate by Parts (30 Problems with High Quality Solutions)

Evaluate the integral using integration by parts with the indicated choices of u and du. 1) &#8747; x ln x dx, u=ln x, du=xdx 2) &#8747; theta sec^2(theta) dtheta, u=theta, du=sec^2(theta) dtheta Evaluate the integral 1) &#8747; x cos 5x dx 2) &#8747; (x)(e)^(-x) dx 3) &#8747; re^(r/2) dr 4) &#8747; t sin 2t dt 5

### Contour Integrals and Residue Theorem

B9. Evaluate the following integrals by substituting z = e^iθ to obtain contour integrals, then use the residue theorem. (i) ∫sin 2θ cos 4θ dθ 0--> 2 pi (ii) ∫sin^2 θ cos^4 θ dθ 0 --> 2pi B10. Evaluate the integral ....by contour integration. Please see the attached file for the fully formatted problems.

### Integration : Definite Integrals and Geometric Formula to Evaluate the Integral ( 3 Problems)

For the problems attached, please sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r >0). Please explain as much as possible.

### Integration

For the problems attached, please sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r >0). Please explain as much as possible.

### Lebesgue Measures, Limits and Integrals

Prove or disprove the following: If f is in L^1[0,1], then limit the integral over [0,1] of x^n*f = 0 as n goes to infinity. I saw a similar example asking to prove that the integral from 0 to 1 of x^2n f(x) dx = 0, and they used algebra of functions generated by {1,x^2}, but we haven't talked about that, so please when you

### Integration, proofs, spline interpolation

7. This problem generalizes the factorial function, as in n!=n(n-1)(n-2)...(2)(1), to more general arguments than just the positive integers. (a) Use integration by parts to show that for any positive integer n, the integral with respect to x from 0 to infinity of xne-x is n! (b) Make a clear case that the integral exists

### Volume of cross vault

Let two long circular cylinders, of diameter D, intersect in such a way that their symmetry axes meet perpendicularly. Let each of these axes be horizontal, and consider the "room" above the plane that contains these axes, common to both cylinders. (In architecture this room is called a "cross vault".) The floor of the cross vau

### Approximate Integrals using the Trapezoidal and Simpson's Rule

1. Approximate the integrals using the Trapezoidal rule. a) Integral from -0.5 to 0 x ln(x+1) dx b) Integral from 0.75 to 1.3 ((sin x)2 - 2x sin x +1) dx 2. Find a bound for error in question 1. using the error formula, and compare this to the actual error. 3. Repeat question 1. using Simpson's rule 4. Repeat ques