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Integrals

Line integrals

See attached page Evaluate the line integrals, where C is the given curve

Integral

See attached page Evaluate the integral by making an appropriate change of variables.

Integration by Parts and Motion in a Particle

A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis. (b) Suppose that its acceleration at time t is a=100(1-t)e^(-1). Show that the particle never moves beyond a c

Integration by Parts: Area and Volume

The figure shows the region bounded by the x-axis and the graph of. Use Formulas (42) and (43). Which are derived by integration by parts? To find (a) the area of this region; (b) the volume obtained by revolving this region around the y-axis. Formula (42) Formula (43). See the attached files.

Integration of the Weibull distribution

I am trying to integrate the attached function ( a version of Weibull distribution). I have the solution in Maple -- I think. But I cannot prove it. Tried Integration by parts but still missing something. Please Integrate with respect to y. If it is not clear from the pdf the function is basically : a/b * y ^ (a-1) * e^(-(y

Integral for area Bounded by Two Functions

The problem reads: 1)Plot the following functions on the same coordinate system with the given domain and range. y = x^4 - 2x^2 and y = 2x^2 -4 <= x <= 4 -2 <= y <= 10 2)I am then to set up the definite integral that gives the area of the region bounded by the graphs of the functions. I had no trouble plotting th

Brownian motion and Ito's formula

Hi, I've attached 2 questions in one file. Thanks. Question 1 hints: Hint 1: you have a process Y and a function, the first instinct should be to try Ito. Hint 2: what would the SDE of a martingale look like? Look at attached lecture note. Question 2 hint: Hint: use the integral version of Ito's formula.

Reimann Sum

1. Write a Reimann sum and then a definite integral representing the volume of the region, uisng the slice show. Evaluate the integral exactly. ... 2. Find the volume of a sphere of radius r by slicing. ... [See attachment for questions.]

Work Done by Vector Field Along Helix and Straight Line

#4 in attached problem set (see attachment). 4. Find the work done by the force field F(x, y, z) = -zi + yj + xk in moving a particle from the point (3, 0, 0) to the point (0, pi/2, 3) along: (a) a straight line (b) the helix x = 3cos(t), y = t, z = 3sin(t).

Integrated integral for volume of a unit cube

Give an iterated integral describing the volume of a unit cube (side length 1) in cylindrical and spherical coordinates.. I just need the integral and a short explanation, I do not need them solved.

application of triple and double integrals

See the attached file for full description. 26. Evaluate the triple integral, where E is bounded by the planes y = 0, z = 0, x + y = 2 and the cylinder y^2 + z^2 =1 in the first octant. Find the volume of the given solid 30. Under the surface z = x^2y and above triangle in the xy-plane with vertices (1, 0), (2, 1), and (4

Volume of solid, triple integral, sperical coordinates

Use spherical coordinates (iterated triple integral) to find the volume of the solid in the first octant whose shape is determined by the graph of the cone z=sqrt(x^2+y^2), the cylinder x^2+y^2=1 and the coordinate planes. NOTE: Please see attachment for original problem (question #4)and work i have done on it so far.

Basic Mathematics Problems Involving Digits and Word Problems

Find the greatest common factor for the following group of numbers: 24, 36, 48 A rectangular picture window is 5ft by 8ft. Polly wants to put a trim molding around the window. How many feet of molding should she buy? (Can you draw a picture?) Write the following in standard form of a number (Hint: use a number char

Integrals, Vector Fields, and Differential Equations

Please see attached 1) To find the general integral of the differential equation, discuss existence et uniqueness and find the particular integral that passes for the point (1;5/2) 2) Considering the linear equation of the 2nd order z'' - (2/x) z' + (2/ x2)z = 10 / x2 , x > 0 .

Learning to Sketch Areas under the Standard Normal Curve

Sketch the areas under the the standard normal curve over the indicated intervals, and find the specified areas. 14. To the left of Z = 0.72 18. To the right of Z = -2.17 24. Between Z = -1.40 and Z = 2.03 34. P (z &#8804; 3.20) 42. P (-1.78 &#8804; z &#8804; -1.23) 46. P (-2.37 &#8804; z &#8804; 0)

Antiderrivatives (Integrals)

Please show any work Find the anti-derivative. 2. f(x) = 5x 4. g(t) = t^2 + t 6. g(t) = t^7 + t^3 8. g(x) = 6x^3 + 4 10. f(x) 5x - (sq rt of x) 12. r(t) = 1/t^2 14. p(t) = t^3 - t^2/2 - t 16. f(t) = 2t^2 + 3t^3 + 4t^4 Fin the indefinite integrals in the following. (all have the symbol for indefini

Lagrange

Please see attachment Compute the Lagrange interpolating polynomial L(x) for the function f(x) f (x) = &#8730;(cos(ax)) a = 1.1125 passing through the points (0, f(0)), (0.5, f(0.5)) and (1, f(1)). Let S1 be the first Simpson' rule approximation to Show that

Newton's Interpolating

See attachment. Use Newton's interpolating polynomial to approximate the function: f (x) = e^ (-ax2) a = 1.1125 Construct approximation using the values f (x) at x= -2, -1, 0, 1, 2. Call this approximation N(x). ii) Compute the value of the integral accurate to 1 decimal place. iii) Compute sufficient trapez

Integration and other topics

See attachment for fomatting 1 Evaluate 3&#8747;1 1-&#8747;-2 (x2y-2xy3)dydx 2 Correctly reverse the order of integration, then evaluate 1&#8747;0 1&#8747;y xeydxdy 3 The plane region R is bounded by the graphs of y=x and y=x2 . Find the volume over R and beneath the graph of f(x, y) = x + y. 4 Find t

Curve of Regression (Part of a Physics Experiment)

I have a defined curve with an associated 2nd order polynomial equation. I want to understand how to calculate the area under the curve as I have it denoted on the attached pdf file. Also is the integration relative to the x,y limits I have shown.....or is it truly the total area under the curve relative to the x-axis? Sho

Area bounded by two curves.

(Please see the attachment for fig.) Let R and S be the regions in the first quadrant shown in the figure. The region R is bounded by the x-axis and the graphs of y = 2 - x^3 and y = tan x. The region S is bounded by the y-axis and the graphs of y = 2 - x^3 and y = tan x. a) Find the area of R. b) Find the area of S

Integration of Functions

Integrate for upper limit 3 and lower limit -3 1) ( 20 / (1 + x^2) - 2 ) dx The 2 is a separate term 2) ( 20^2/ (1 + x^2)) ^2 - 4 ) dx Note. Both numerator and denominator are squared The 4 is a separate term 3) ( 20/ (1+x^2) - 2 )^2 dx The 2 is a separate term 4) Integrate

The area of the region bounded by two curves

Please see the attached file. Part a. Graph the region bounded by y = 12 - x^2 and y = -x Part b: Give a formula in terms of x-integral(s) for the area of this region. Do not compute the area. Part c: Give a formula in terms of y-integral(s) for the area of this region. Do not compute the area.

Definite Integral and Area

Two questions on definite integral and area. See the attached file. 3. Read the statement of this problem very carefully. The graph of g(x) is given below on the interval [-3,5]. Regions A, B and C are labeled in the graph. The area of region A is 32/3, the area of region B is 32/3, and the area of region C is 32/3. Co