### Line integrals

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

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

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

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

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.

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

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

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.

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.]

#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).

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.

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

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.

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

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 .

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 ≤ 3.20) 42. P (-1.78 ≤ z ≤ -1.23) 46. P (-2.37 ≤ z ≤ 0)

Definite Integrals - Work out the given definite integrals. (See the attached questions file).

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

Please see attachment Compute the Lagrange interpolating polynomial L(x) for the function f(x) f (x) = √(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

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

See attachment for fomatting 1 Evaluate 3∫1 1-∫-2 (x2y-2xy3)dydx 2 Correctly reverse the order of integration, then evaluate 1∫0 1∫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

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

(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

(See the 2 graphs in the attached question file) I need to solve for the area under the 2 noted curves. In the first graph, the beginning x,y coordinate is 0 minutes; 80 degrees F; the ending x,y coordinates are 4.5 minutes; 212 degrees F In the second graph, the beginning x,y coordinate is 5.0 minutes; 213 degrees; th

See attached page for problem.

See attached for integration value tables and derivatives

Integrate x^2 sin(sqrtx)dx

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

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.

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

Please see the attached file. find the area of the region bounded between the graphs of...