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Let R be the region bounded by the curves: f(x) =ln(x+3) + 2 and g(x) = x^2 -8x + 18 Find the area of R. Show all work including integrals used and limits of integrations.

Integral calculus

Solve the given integral using integration by parts method. Integrate ∫x^2e^(3x) dx

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

Double integrals problem

Would you please give me a detailed solution to the attached problem? 2) Let R be the region bounded by the graphs of y = x - sin x, y = π, and x = 0 a) Sketch the region R. b) Use a double integral to calculate the area of the region R.

One dimentional 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,

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


Use partial decomposition to integrate (x-7)/(x^2-x-12 ) (5x)/(2x^3+6x^2 ) (x^3-8x^2-1)/(x+3)(x^2-4x+5)


Use partial decomposition to integrate. (2x^2-x-20)/(x^2+x-6 ) (sint)(4cos^2t-1)/(cost)(1+2cos^2t+cos^4t) (x+pi )/(x^2-3pix+2pi^2)

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