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Integrals

Graph : Finding the Area of a Shaded Region

(See attached file for full problem description with image) The graph below represents the function f(x) = x3 + 2x2 - 5x - 6. Explain how you process the calculation of the shaded region.

Integration of exponential

Integration of exponential: I am having difficulty integrating exponential. I want to compute the indefinite integral of r`(t) where r`(t) is the vector <3, -e(^ -t), 0> The first integration I have is <3t+c1, ------- c3> I am not sure how to integrate the -e^-t ------------------------------------------

Converting a double integral into a triple integral.

I have a double integral of the form I from 0 to 2 and I from 0 to y (4-y^2) dx dy How does one convert this double integral into a triple integral? keywords: integration, integrates, integrals, integrating, double, triple, multiple

Finding area under normal curve

Find the area under the normal curve which is shaded on the graph. Use 4 decimal places. See attached file for full problem description.

Integral calculus to solve differential equation problems

1. The United States Census Bureau mid-year data for the population of the world in the year 2000 was 6.079 billion. Three years later, in 2003, it was 6.302 billion. Answer the following questions. (See attached bmp file) 2. A metal ball, initially at a temperature of 90 C, is immersed on a large body of water at a temperat

Integral Creation

Create an integral whereby you are forced to use all four types of integration. Work the problem and explain why each (u-substitution, trig substitution, fractions, parts) are all needed. this must be only one integral, that is it must all be under a singular fraction and cannot be the sum such as integral of lnx+arctanx dx or

Integration and Simpson's Rule

(See attached file for full problem description with proper symbols and equations) --- A. Evaluate the improper integral: Infinity ∫ (xe^x^2)dx 0 B. Complete the square, then use integration tables to evaluate the indefinite integral: ∫ {(sqrt(x^2 + 6x + 13))/x+3}dx C. Which of the following would

Integration: volume of solid

Let f and g be the functions given by f(x) = 1 + sin(2x) and g(x) = e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x).

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 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

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

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? ---

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

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

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