### Potential Equation on a Disc : Dirichlet

Solve the potential equation on a disc... (See attachment for full question)

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Solve the potential equation on a disc... (See attachment for full question)

Calculate to show, for f of class C2 ... {see attachment} What is the integral on the right equal to {see attachment}

Interpret the attached iterated integrals as a triple integral for the appropriate region {see attachment}, sketch {see attachment} and change the order of integration so that the innermost integral is taken with respect to y. (f is continuous) ... **See attachment for complete question.

Evaluate the definite integral from x = 2 to x = 3 of: f(x) = 6x^2 - x - 6

Please see the attached equation. 0 ---> -2 ∫2x3 -4x dx

Please see the attached equation. 4 --> 1 ∫5x dx

Integrated from 0 to 4 : 3x^2 dx

Integrate (3x+1)^1/2 dx rewrite as Integrate (3x+1)^1/2 1*dx use chain rule with inserting coefficient.

Integrate (x^3+2x^2)^8(3x^2+4x)dx. Use the chain rule.

Integrate 6 sqrt x dx.

Integrate (6x^2-4x^3+5x^4)dx

Find the area under the curve y=-x^2+3x from x=1 to x=4

Consider the attached differential equation where I = (a,b) and p,q are continuous functions on I. (a) Prove that if y1 and y2 both have a maximum at the same point in I, then they can not be a fundamental set of solutions for the attached equation. (b) Let I = {see attachment}. Is {cos t, cos 2t} a fundamental set of solu

Thank you in advance for your help in solving this problem. See attached problem statement.

Derive the composite midpoint method and composite error.

Please evaluate the attached by means of the residue theorem.

See attached... Let g(a) be the real solution to x+x^5=a

Please assist me with the attached problems relating to finding the region within a curve. 3. (a) Obtain an expretsian far Calculating the area between the curve y=2?x+x2 and the u-axis far 0 <x< 2 by dividing the area up into 2n strips of equal width (each strip will have width 1/n) and then taking the limit as n ---> infini

Find the centroid of the first octant region that is interior to the to the two cylinders x^2+z^2=1 and Y^2+Z^2=1 centroid for x y and z are x'=1/M*triple integral of x^2*dV y'=1/M*triple integral of y^2*dV z'=1/M*triple integral of z^2*dV

See attached file

Evaluate the integral in the following: ∫(2-x)^3/5*dx

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

(a) Describe how the weights for the order 4 closed Newton-Cotes quadrature formula could be found. Do NOT calculate the weights. (b) What are composite quadrature rules and why are they preferred to using higher order quadrature rules? (c) What are the main characteristics of a predictor-corrector method for solving an initia

A) For what simple closed (positively oriented) curve C in the plane does the line integral of (e^(-x)+ 4x^2y +y)dx + (x^3-x*y^2+5x)dy have the largest positive value? (use Green's theorem) b) Determine what this value is.

Problem: Given the power series for the following function (1+x)^k (a) Write the power series for (1+x)^(1/3) (b) Use the power series from part (a) to find the power series for x^3 (c) Using this series approximate the following integral (1+x^3) ^(1/3) using the first three terms

(a) Use the integral definition of the Laplace transform to compute (FUNCTION1) (b) A function g(t) has the transform (FUNCTION2). Use transform properties to compute the following. Express each in simplest form: i) (FUNCTION3) ii) (FUNCTION4) (See attachment for full question).

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)

Consider the vector field F=((x^2)*y+(y^3)/3)i,(i is the horizontal unit vector) and let C be the portion of the graph y=f(x) running from (x1,f(x1)) to (x2,f(x2)) (assume that x1<x2, and f takes positive values). Show that the line integral "integral(F.dr)" is equal to the polar moment of inertia of the region R lying below

Using the coordinate change u=xy, v=y/x, set up an iterated integral for the polar moment of inertia of the region bounded by the hyperbola xy=1 , the x-axis, and the two lines x=1 and x=2. Choose the order of integration which make the limits simplest THIS MESSAGE IS ADDRESSED TO ANY TA: I found something , I just want you

See attached explanation