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Integrals

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

Stokes Theorem, Curl and Positively Oriented Hemisphere

7) Use Stoke's Theorem to evaluate curl F*dS S is the hemisphere oriented in the direction of the positive x-axis. 8) Use Stokes Theorem to evaluate C is the boundary of the part of the plane 2x + y + 2z = 2 in the first octant. 9) Suppose that f(x,y,z)= , where g is a function of one variable such that g(2) = -

Green's Theorem, Positively Oriented Curve, Ellipse

Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. ∫c xdx + ydy. C consists of the line segments from (0,1) to (0,0)...and the parabola y = 1 -x^2.... Use Green's theorem to evaluate the line intgral along the positively oriented curve. ∫c sin y dx + x cos y dy

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+≡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≡11(mod 17) using the table in 7. 9.

Helicoid Integral

Evaluate ∫∫S √(1 + x^2 + y^2) dS where S is the helicoid: r(u,v) = u cos(v)i + u sin(v) j + vk , with 0 ≤ u ≤ 3, 0 ≤ v ≤ 2pi. Please see the attached file for the fully formatted problem.

Flux Integrals

Suppose is a radial force field,... is a sphere of radius...centered at the origin, and the flux integral.... Let be a sphere of radius... centered at the origin, and consider the flux integral... . (A) If the magnitude of... is inversely proportional to the square of the distance from the origin,what is the value of..

Newton's Law of Cooling : Average Temperature

If a cup of coffee has temperature 95 degrees Celsius in a room where the temperature is 20 degrees Celsius, then according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t)=20+75e^(-t/50). What is the average temperature of the coffee during the first half hour?

Lebesgue Integral and Monotone Convergence Theorem

Let f be a nonnegative integrable function. Show that the function F defined by F(x)= Integral[from -inf to x of f] is continuous by using the Monotone Convergence Theorem. From Royden's Real Analysis Text, chapter 4. See the attached file.

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

Definite and indefinite integrals

Thank you in advance for your help. Evaluate the following definite and indefinite integrals: (1)The integral of (2x)/([x^2]+1)dx (2)The integral of [(arctan(x))/([x^2]+1)]dx (3)The integral of sqrt([x^3]+[1x^5])dx (4)The integral of (2+x)/([x^2]+1)dx (5)The integral of (2x)/([x^4]+1)dx (6)The integral from 0 to 2 of (x

Proving an Integral Equation

If f is continuous for all real numbers, prove that the integral from a to b of f(x+c)dx=the integral from a+c to b+c of f(x)dx. For the case where f(x) is greater than or equal to 0, draw a diagram to interpret this equation geometrically as an equality of areas.

Integrals : Rate of Change Word Problem

Water flows from the bottom of a storage tank at a rate of r(t)=200-4t liters per minute, where 0 is less than or equal to t and t is less than or equal to 50. Find the amount of water that flows from the tank during the first 10 minutes.

Work Done by Radial Vector Field Along a Curve

If C is the curve given by r(t) = (1 + 3 sin t) i + (1 + 5 sin^2 t) j + (1 + 5 sin^3 t) k, 0 ≤ t ≤ π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.

Integral of a Contour

Calculate the following integrals: ∫ from 0 to ∞ x^¼/(x²+9) dx Please see attached for proper format.

Residues and Closed Contours : Solve the Integral

Calculate the following integral... Please see attached for full question. Solution. Consider a close contour C shown above, where C consists of and a line segment from -R and R. Consider positive orientation, namely, clockwise. Choose r large enough so that are in the region covered by C. Let . By residual Theorem

Integrals : Riemann Sum with Diagrams

This question has me going around in circles. I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it. (a)Find an approximation to the integral as 0 goes to 4 of (x^2-3x)dx using a Riemann sum with right endpoints and n=8. (b)Draw a diagram

Elementary Numerical Analysis

GAUSSIAN NUMERICAL INTEGRATION 1. Consider approximating integrals of the form... in which f(x) has several continuous derivatives on [0, 1] a. Find a formula... which is exact if f(x) is any linear polynomial. b. To find a formula... which is exact for all polynomial of degree ≤ 3, set up a system of four e

Arc Length of Curve, Tangent Line, Limits and Solid Revolution

1. Find the volume of the solid generated by revolving the region enclosed by: {see attachment} 2. Find the arc length of the graph of the curve {see attachment} 3 - 7. Integrate attached equations ... 8. Find the limit of the improper integral: {see attachment} 9. Find the arc length of the curve given in parametric