### Integration by Substituton

I am having problems understanding how to solve linear equations. For example, dy/dt = -4y + 3e^-t Can you solve this step-by-step so that maybe I can understand how to do it myself?

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I am having problems understanding how to solve linear equations. For example, dy/dt = -4y + 3e^-t Can you solve this step-by-step so that maybe I can understand how to do it myself?

1.) For the arithmetic sequence {-10,-2,6,14,}, find: a.) a recursive rule for the nth term b.) an explicit rule for the nth term 2.) For the geometric sequence {512,256,128,64,...}, find: a.) a recursive rule for the nth term b.) an explicit rule for the nth term 3.) Determine whether each of the follo

1. Find the curl of the vector field F at the indicated point: 2. Evaluate the following line integral using the Fundamental theorem of line Integrals: 3. Use Green's Theorem to calculate the work done by the force F in moving a particle around the closed path C: 4. Find the area of the surface over the part of the

Find the volume of the solid bounded by x = 0, y = 0, z = 0 and x + 2y + 3z = 6 by triple integration. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -∞ and ∞. I1 = ∫ df / [α2 + (2πf)2] I2 = ∫ sinc2(τf) df I3 = ∫ df / [α2 + (2πf)2]2 I4 = ∫ sinc4(τf) df

Please help with the following problems. Please provide step by step calculations and diagrams. For the following problem, sketch the region and then find the volume of the solid where the base is the given region and which has the property that each cross-section perpendicular to the x-axis is a semicircle. 1) the regio

Evaluate the integral of several trigonometric functions.

Determine where the function f(x) = x + [|x^2|] - [|x|] is continuous I don't understand how to work this problem. Can someone show and explain how to solve this problem in detail? I've asked for help on this problem before but I still don't understand it. The function is continuous everywhere but 0. I don't understan

Do the following: (1) Evaluate Int(P(x, y) dx + Q(x, y) dy) over the curve C, where P(x, y) = y^2, Q(x, y) = 3x, and C is the portion of the graph of the function y = 3x^2 from (-1, 3) to (2, 12). Here, "Int" stands for integral. (2) Use the Divergence Theorem to evaluate the surface integral Int(F*n ds) over the surface S

See attached file for full problem description.

1 Find the area of the part of the surface 2z = x^2 that lies directly above the triangle in the xy-plane with the vertices at (0,0),(1,0) and (1,1). 2 Find the volume of the region in the first octant that is bounded by the hyperbolic cylinders xy = 1, xy = 9, xz = 4, yz = 1, and yz = 16. Use the transformation u = xy, v =

Let F = (2x, 2y, 2x + 2z). Use Stokes' theorem to evaluate the integral of F around the curve consisting of the straight lines joining the points (1,0,1), (0,1,0) and (0,0,1). In particular, compute the unit normal vector and the curl of F as well as the value of the integral:

Suppose that a tank initially contains 2000 gal of water and the rate of change of its volume after the tank drains for t min is '(t)=(0.5)t)-30 (in gallons per minute). How much water does the tank contain after it has been draining for 25 minutes? keywords: integration, integrates, integrals, integrating, double, triple, m

The region R is bounded by the graphs of x-2y = 3 and x=y^2. Set up (but not evaluate) the integral that gives the volume of the solid obtained by rotating R around the line x=-1.

Let S be the closed surface of the paraboloid of revolution z = ±(4 − x2 − y2 ) where −2 x, y +2. Evaluate the following surface integral directly and then by using the divergence theorem; where R is the position vector to a point on the surface and is the outward pointing normal at that point. See att

1. Find the inverse of F(s) = s/[(s+1)(s^2+4)] the answer can be left as a convolution integral 2.Solve y''+y'+(5/4)y=y(t) y(0)=y'(0)=0 using LaPlace Transforms sin(t) t greater or equal to 0 or less than Pi y(t) { 0 t greater or equal than Pi

The problems in the file submitted are from an undergraduate course in real Analysis. If you are able to work the problems, please detail any theorems or lemmas used in your solutions. The book we are using is titled "The Elements of Real Analysis" by Robert G. Bartle. We are working on derivatives and integrals, but have not

If a>0 show that pi lim ∫ sin(nx)/nx dx = 0 a What happens if a = 0. The problem in the file submitted is from an undergraduate course in Real Analysis. If you are able to work the problems, please detail any theorems or lemmas used in your solutions.

The problems in the file submitted are from an undergraduate course in real Analysis. If you are able to work the problems, please detail any theorems or lemmas used in your solutions. The book we are using is titled "The Elements of Real Analysis" by Robert G. Bartle. We are working on derivatives and integrals, but have not

Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Suppose that the double integral of f(x, y) dA = 4, where D is the disk x^2 + y^2 <= 1. Now suppose E is the disk x^2 + y^2 <= 9 and 9(x,y) = 3f(x/3, y/3). What is the value of the double integral of g(x, y) dA? Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, in

Find the volume of the solid that lies within the sphere , above the plane, and outside the cone . Please see the attached file for the fully formatted problems.

(1) Find the indicated roots: (a) The eighth roots of 1 and (b) The cube roots fo 1+ i (2) By considering the real and imaginary parts of the integral in part (1), evaluate the integral e^(1+i)x dx.

(1) S cos2xsin2xdx (2) S tan2xsecxdx (3) S sinxcosxdx using four different methods

1 Write the Taylor polynomial with center zero and degree 4 for the function f(x) = e^-x 2 Determine the values of p for which the series ∞ Σ 1/(2p)ⁿ n=1 3 Calculate the sum of the first ten terms of the series, then estimate the error

Approximate the integral using the trapezoid reduction formula with m=4. (Do by hand). Find the exact value of the integral and the exact error. See attached file for full problem description. keywords: integration, integrates, integrals, integrating, double, triple, multiple

2 Use Romberg integration and compute A33 to approximate the integral ∫ x ln x dx where m=3. Please show all work.

(4.3) 4d Find a bound for the error using Simpson's rule and compare this to the actual error for the following integrals (4.4) 2b Use the composite Simpson's rule to approximate the following integrals. , n = 4 Please see the attached file for the fully formatted problems.

Let f(z) be holomorphic on the unit disc and f(0)=1. By working with 1/2ipi(integral over unit circle of [2+,-(z+1/z)]f(z) dz/z) prove that a)2/pi(integral(0 -2pi) of f(e^itheta)cos^2theta/2 d(theta))=2 + f'(0) b)2/pi(integral(0-2pi) of f(e^itheta)sin^2theta/2 d(theta))=2-f'(0)

Prove that integral (0 to pi/2) of sin^2n theta d(theta)=pi(1x3x5x...2n-1)/2(2x4x6x...2n)