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Integrals

Volume of cross vault

Let two long circular cylinders, of diameter D, intersect in such a way that their symmetry axes meet perpendicularly. Let each of these axes be horizontal, and consider the "room" above the plane that contains these axes, common to both cylinders. (In architecture this room is called a "cross vault".) The floor of the cross vau

Approximate Integrals using the Trapezoidal and Simpson's Rule

1. Approximate the integrals using the Trapezoidal rule. a) Integral from -0.5 to 0 x ln(x+1) dx b) Integral from 0.75 to 1.3 ((sin x)2 - 2x sin x +1) dx 2. Find a bound for error in question 1. using the error formula, and compare this to the actual error. 3. Repeat question 1. using Simpson's rule 4. Repeat ques

Complex integration using series expansion of analytic functions

I want to check my answer: Evaluate the following integrals: integral over gamma for (sin z)/z dz, given that gamma(t) = e^(it) , 0=<t=<2pi ( e here is the exponential function) My work: sin z = z - z^3/3! + z^5/5! + ... + (-1)^n (z^(2n-1))/(2n-1)! + ... divide by z we get (sin z)/z = 1 - z^2/3! + z^4/5!

Complex Integration using power series expansion of analytic functions

Evaluate the following integrals: (a) integral over gamma of (e^z - e^-z)/(z^n) dz, where n is positive integer and gamma(t) = e^(it), 0 =< t =< 2 pi (b) integral over gamma of (dz/(z^2 + 1) ) where gamma(t) = 2e^(it), 0 =< t =< 2pi ( Hint: expand (z^2 + 1)^-1 by means of partial fractions PLEASE USE POWER SERIE

Triple Integral on Specific Solid

Compute a triple integral over a specific solid that would be very difficult in rectangular coordinates, but easy in parabolic cylindrical coordinates, u, v, z, where x=(1/2)(u^2-v^2) y=uv z=z You must come up with the solid. Remember that the Jacobian determinant (u^2+v^2) must be used when transforming an integral to this

Interpolate

(See attached file for full problem description with proper equations) --- 1. For medical purposes the level of sugar was measured in blood (in mg/dl). The samples were taken with 1/2 hour increments, as the following table shows: Initial sample 96 mg/dl After 30 min. 133 mg/dl After 60 min. 142 mg/dl After 90 min.

Area Bounded by Curves & Volume of Solid of Revolution

Find the area of each polar region enclosed by f(theta) for a <=theta<=b 36) f(theta) = theta/pi, 0<=theta<=2pi PLEASE SHOW EVERY STEP IN SOLVING THESE-NO COMPUTER PROGRAMS PLEASE. 4) Identify each curve as cardiode, rose(state # of petals), leminscate, limacon, circle, line or none of above. a) r=2sin2theta b) r^2=2c

Integrals Application Word problem : Supply and Demand Curves and Equilibrium

4. The demand curve for a product has equation p=20 e^(-0.002q) and the supply curve has equation p=0.02q + 1, where q is the quantity and p is the price in $/unit. a) Which is higher the price at which 300 units are supplied or the price at which 300 units are demanded? Find both prices. b) Sketch the supply and deman

Definite Integrals : Supply and Demand Curves and Equilibrium

6. The demand curve for a product has equation p = 100 e^(-0.008q) and the supply curve has equation p = (4&#8730;q) + 10 , where q is the quantity and p is the price in dollars/unit. a) At a price of $50, what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push price

Definite Integrals Application Word Problem : f(t) = 100e^(-0.5t)

A service station orders a 100 cases of motor oil every 6 months. The number of cases of oil remaining t months after the order arrives is modeled by f(t) = 100e^(-0.5t) a) How many cases are there at the start of the six-month period? How many cases are left after the end of the six-month period? b) Find the average number

Vector Calculus: Surface Integral

#12) Surface integrals; &#61682;s&#61682; G(r) dA. Evaluate these integrals for the given data. (show the details.) G=cosx + siny, S: the portion of x+y+z=1 in the first octant (See attached file for full problem description with equations) Question in Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.

Normed Space, Compactness and Transformation

Let X be a normed space, I closed interval ( or half-open on the right) and a = inf I, b = sup I. Let h : I -> [0,infinity) be a continuous function such that integral ( from a to b ) h(t)dt < positive infinity where integral from a to b represents the improper integral when I is not closed. Let epsilon > 0 and

Solving a Pfaffian equation for a complete integral

Hello. Thank you for taking the time to help me. I cannot use mathematical symbols, thus, * will denote a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. To simplify things, I will let p=u*x and q=u*y. Furthermore, I will use ^ to denote a power. For example, x^2 means x squared. Also,

Green's function and Poisson's integral formula

Hello. Thank you for taking the time for helping me. The following is the problem which I need to solve (there are actually two parts): I need to construct Green's function for the Dirichlet problem (Laplace's equation) in the upper half plane R={(x,y) : y>0} and I must derive Poisson's integral formula for the half plane.

Business statistics and calculus

Please see attached. Hi, I am having trouble doing these problems listed below. Please show me how to solve these problems for future reference. Thank you very much. I would like for you to show me all of your work/calculations and the correct answer to each problem. For Exercise 2, find the mode of the probability

Computing areas and volumes using multiple integrals.

(1) Find the volume of the solid bounded by the paraboloid x2 + y2 = 2z, the plane z = 0 and the cylinder x2 + y2 = 9. (2) Find the volume of the region in the first octant bounded by x + 2y + 3z = 6. (3) Find the area of the solid that is bounded by the cylinders x2+z2 = r2 and y2+z2 = r2. (4) Find the volume enclosed by t

Revenue Function and Definite Integral of Revenue Function

Revenue at day D = (200 + 10D - 100P)*P D refers to the day, with Monday being 1, Tuesday 2, etc up to Friday with a value of 5. The assignment is as follows: 1. If you are charging $1 per cup, what is your revenue for each of the five days? What is your total revenue for the week? 2. What is the indefinite integral

Integration Techniques and Applications

1. Find the indefinite integrals for the following functions: a. f(X) = 10000 b. f(X) = 20X c. f(X) = 1- X2 d. f(X) = 5X + X-1 e. f(X) = 12- 2X f. f(X) = X3 + X4 g. f(X) = 200X - X2 + X100 2. Find the definite integral for the following functions: a. f(X) = 67 over the interval [0,1] b.

Definite Integral as the Limit of a sum BrainMass Expert explains

Calculus Integral Calculus(I) Definite Integral as the Limit of a sum Method of Summation Definite Integral It is an explanation for finding the integral by using the method of summation(part I). Find by the method of summation the value of: (a) ∫ e^( - x)dx, where the lower limit is a and the upper limit is b

Congruences, Primitive Roots, Indices and Table of Indices

6. Let g be a primitive root of m. An index of a number a to the base (written ing a) is a number + such that g+&#8801;a(mod m). Given that g is a primitive root modulo m, prove the following... 7. Construct a table of indices of all integers from.... 8. Solve the congruence 9x&#8801;11(mod 17) using the table in 7. 9.

Solve Sequences Used in Given Situation

There is a rope that stretches from the top of Maidwell building to a tree on the racecourse, and the length of this rope is 1km. A worm begins to travel along the rope at the rate of 1cm each second in an attempt to get to the other end. then a strange thing happens... some malevolent deity intervenes to make life even hard

Evaluating integrals

Evaluate the following integrals: (1)The integral of (6sin[2x])/sin(x)dx=____+C (2)The integral of (7-x)(3+[x^2])dx=____+C (3)The integral from 3 to 7 of ([t^6]-[t^2])/(t^4)dt=____+C (4)The integral of (6sin[x])/(1-sin^2[x])dx=____+C