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Integrals

Applications of integration

Let R be the shaded region bounded by the graphs of y=sqaure root of x, and y=e to the power of -3x, and the vertical line x=1. a) Find the area R b) Find the volume of the solid generated when R is revolved about the horizontal line y=1. c) The region R is the base of a solid. For this solid, each cross section perp

Volume of a Solid of Revolution by Shell Method

Approximate the volume of the solid generated by revolving region formed by the curve y=x^2, x-axis and the line x=2. Volume approximated by concentric shells a) Sketch the reqion y=x^2, x-axis and the line x=2. b) We'll approximate the volume revolving the region about the y-axis. c) partition the interval [0, 2) in x,

Quantitative Methods Questions

I have completed the answers to the questions. I just need to have someone confirm that they are correct. Thank you! True/False Indicate whether the sentence or statement is true or false. F 1. Management science is the application of a scientific approach to solving management problems in order to h

PID (Proportional / Integral / Derivative) Control System

Consider the system shown in Fig.1. (attached file) This is a PID control of a second-order plant G(s). Assume that disturbances D(s) enter the system as shown in the diagram. It is assumed that the reference input R(s) is normally held constant, and the response characteristics to disturbances are a very important consideration

Integration / Anti-derivative (8 Problems)

Please show how to solve each of the following problems. Find the antiderivative (integral) 6. (x^2/the square root of [x^3-4])dx 8. (x^2 - 2)^3 2x dx 9. sin^3(x)dx 10. x^3/x^2 + 1 dx 11. 1/xln x dx 12. ln x/x dx 14. 2x + 1/square root of [x + 4] dx

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

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

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. ∫dr/r√(r²-9)

Integration Using Formulas : ∫2dx/x√(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. ∫2dx/x√(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 ∫ 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: ∫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

Integration by parts

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

Surface area of revolving curve

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

Changing the Order of Integration and Finding the Volume

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