### Monte Carlo integration

Describe how to use the Monte Carlo method to estimate the double integral of xydxdy over the area 0<x<y and 2<y<4

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Describe how to use the Monte Carlo method to estimate the double integral of xydxdy over the area 0<x<y and 2<y<4

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Find the explicit solution to the ODE 2yy'=(1+y^2) subject to y(0)=4. What is the solution if y(0)=-4? *(Please see attachment for proper citation of symbols and numbers)

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See attached explanation

Please assist me with the attached problems relating to functions and integrals - thank you!

Prim is primitive! In genral the moment of inertia around an axis( a line) L is: Isubl=double prim (dist(.,L)^2*delta*dA) The collection of lines parallel to the y axis have the form x=a .Let I=Isub(y) be the usual moment of inertia around the y axis I= double prim of x^2*delta*dA Let I(bar) be the moment of ine

Compute the mass, centroid, and moments Ix, Iy and Io of the half-disk: y>0, x^2+y^2<1 with density delta(x,y)=y it is said we should know the primitive (sin(x))^n or (cos(x))^n from Pi/2 to 0

Find the integral of f(x,y)=x^2 over the domain D which is bounded by y=3x, x=3y and x+y=4 Hint: use the transformation x=3u+v and y=u+3v

Find the integral over C of f(x,y) = x^2 where C is the unit circle

Evaluate integate (3sin2x - 2cos3x)dx a=pi/4 and b=pi/2

Evaluate the attached integral: a) Write an equivalent iterated integral with the order of integration reversed. b)Evaluate this new integral and check that your answer agrees with part (a)

Please see the attached file for full problem description. --- Find the volume of the region that lies under the graph of the paraboloid z = x^2 + y^2 + 2 and over the rectangle R = {(x, y) | -1 and in two ways (a) by using Cavalieri's principle to write the volume as an iterated integral that results from slicing

Find by the method of summation the value of : a) The integral (from 0 to 1) of the square root of x. (dx) b) The integral (from 1 to 4) of 1 divided by the square root of x. (dx) Please view the attachment for proper formatting.

Integration as the limit of a sum (II) Find by the method of summation the value of: a) The integral (from 0 to 1/2*pi) of sin(x). b) The integral (from a to

See Attachment for equation We know that sin z and cos z are analytic functions of z in the whole z-plane, what can we conclude about *(see attachment for equations)* in the first quadrant

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Please see the attached file for the fully formatted problems.

Please help with various Calculus questions. (please see attachment)

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(-x(t^2))*((-2(x^2)t)^4)

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A trough is 2 meters long, 2 meters wide, and 2 meters deep. The vertical cross-section of the trough... (See attached)

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The problems are attached 1 -5 based on Chapter Partial Derivative - (Maximum & Minimum Values and Lagrange Multipliers 1. Locate all relative maxima, relative minima, and saddle points of the surface defined by the following function. 2. Consider the minimization of subject to the constraint of (a) Draw the

If f(θ) is given by: f(θ)=6cos^3θ and g(θ) is given by: g(θ)=6sin^3θ Find the total length of the astroid described by f(θ) and g(θ). (The astroid is the curve swept out by (f(θ), g(θ)) as θ ranges from 0 to 2pi)