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    Integrals

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    One dimensional unsteady diffusion

    (See attached file for full problem description) 5.7 a) Consider one-dimensional unsteady diffusion in an absorbing medium. The causal fundamental solution E with pole at x = 0, t=0 satisfies Reduce the problem to ordinary diffusion by the transformation E = b) What would be the significance of the problem in which q^2

    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,

    Finding the centroid of a lamina using definite integrals.

    A lamina (with uniform thickness 0.01m) has the shape in the xy plane bounded by the curves y-4-x^2, y=0, If the density given is constant, find the centroid. Please see the attached file for the fully formatted problems. integrals, integrating

    Applications of Integrals: Area of a Region

    Let R be the shaded region in the first quadrant enclosed by the graphs of y=e^(-x^2), y= 1-cos x, y-axis as shown in the figure above. (a) Find the area of the region R. (b) Find the volume of the solid generated when the region R is revolved about the x-axis. (c) The region R is the base of a solid. For this solid, each cr

    Finding Areas of Regions Bounded by Three Lines and Solid

    Let R and S be regions in the first quadrant. R is bounded by the x-axis, y=2-x^3 and y=tan x. S is bounded by the y-axis, y=2-x^3 and y=tan x. a) Find area of R. b) Find area of S c) Find volume of the solid generated when S is revolved about the x-axis.

    Integrating using the Midpoint Rule; Eliminating Parameters

    1.) Estimate integral from (0 to 2) of 1/(2+x^2) dx using the midpoint rule n=4 2.) Eliminate parameter of parmetric equation x=cos theta y= sin ^2 theta sketch the Cartesian graph equal to 0 less than or equal to theta less than or equal to sin pi/2 3.) 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

    Ski Jump Problem (projectile)

    At time t = 0 a skier leaves the end of a ski jump with a speed of Vo feet per second at angle alpha with the horizontal. Position vector of the skier is represented by the vector : r(t) = [Vo (cos theta) t] i + [h + (Vo sin theta) t - 1/2gt^2] j The skier lands 259 feet down the incline 2.9 seconds later. (g = 32 ft. per sec^2

    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

    Integration of Function

    Solve the integral equation: y(x) = 1 + integral from 0 to x of ( y(t)*t^2 dt) (in the integral is y as a function of t times t^2). See the attached file.

    Viciously Damped Single-Degree-of-Freedom System

    Derive the response of a viciously damped single-degree-of-freedom system of force Ft=F0e^-αt u(t) by means of a convolution integral. Plot the the response for the system parameters m=12 kg, c= 24 N.s/m, k=4.800 N/m and the force paramters F0=200 N, α=1 Prescribed Textbook: Fundamentals of vibrations: Leonard Meirovitch

    Convolution Integral : Viciously Damped Single-degree-of-freedom System

    Derive the response of a viciously damped single-degree-of-freedom system of force Ft=F0e^-αt u(t) by means of a convolution integral. Plot the the response for the system parameters m=12 kg, c= 24 N.s/m, k=4.800 N/m and the force paramters F0=200 N, α=1 Prescribed Textbook: Fundamentals of vibrations : Leonard