### Integration Problems

-2 1. Evaluate ∫ (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

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-2 1. Evaluate ∫ (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

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

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

(See attached file for full problem description)

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. ∫(2θ³-7θ²+7θ)/(2θ-5) dθ

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 π/2≤x≤pi Please show each step in the problem. Thank you. ∫√(1-sin²θ)dθ

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. ∫dr/r√(r²-9)

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. ∫2dx/x√(1-4ln²x) integrate

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

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

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

(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

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. 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)

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)

In this problem I am asked to use integration by parts utilizing the formula: ∫udv = uv - ∫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. ∫4xsec²2xdx

In this problem I am asked to use integration by parts utilizing the formula: ∫udv = uv - ∫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. ∫x³lnxdx 1≤x≤e

Using the formula for the surface area of a revolving curve about the x-axis: S=∫2πy√(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=√(x + 1) 1≤x≤5 Please be detailed, showing the compl

Please see the attached file for the full problem description. --- 1. Transform the given integral in Cartesian coordinates to one in polar coordinates and evaluate the polar integral. : refer to integral 5. 2. Determine the values of the given integrals, where W is the region bounded by the two spheres x^2 + y^2 + z^2 = a^

Please see the attached file.

Assuming r, θ are the polar coordinates, change the order of integration: ∫-pi/2-->pi/2 ∫0-->a cos θ f(r, θ ) dr dθ Find the volume of the ellipsoid: x^2/a^2 + y^2/b^2 + z^2/c^2 ≤ 1 Let a and b be any numbers such that a^2 + b^2 =1 and f(x,y) be a continuous function of one variable. Perform the change of

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

∫(pi/2 to 0) sin^4(x) dx -- do not use reduction forumulas use 1-cos2u/2=sin^2x ∫3x^3/sqrt(8-x^2) dx Integrate, integration

Evaluate each of the following integrals: 1. ∫0-->2 6/(5x+2) dx 2. ∫1-->3 e^(-0.4t) dt 3..... 4.... Please see the attached file for the fully formatted problems. Integrate, Integration

Problem 1 and 2: Sketch the region of integration, reverse the order of integration, and evaluate both iterated integrals. ∫0-->2 ∫0-->4-y2 x dx dy ∫0-->pi/2 ∫0-->cosx sin x dy dx Problem 3: When you reverse the order of integration, you should obtain a sum of iterated integrals. Make the reversals and

F(x,y,z)=y ; W is the region bounded by the plane x+y+z=2, the cylinder x^2 + z^2 = 1, and y=0. Integrate the given function over the indicated region W.

1. Using the integral ∫-1-->1 ∫x^2-->1 ∫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

I have a function (see attached). I need to integrate it over m from - infinity to infinity, h from - infinity to infinity. I need to apply a technique such that the integral takes a simple form, easy for integration. The main problem here as you can see is product of terms in the denominator. See the attached file.

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

Please see the attached file for the fully formatted problems.