Explore BrainMass

Explore BrainMass

    Integrals

    BrainMass Solutions Available for Instant Download

    Surface Area

    Surface Area of the Portion of the Plane. See attached file for full problem description.

    Integral convergence or divergence

    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

    Displacement of a Body

    Mechanical System - Displacement of a Body. See attached file for full problem description.

    Integrals : Mean Value

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

    Double Integrals and Integral of a Disk

    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.

    Integral e^(1+i)x dx and roots of 1 and (1+i)

    (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.

    Contour Integrals

    Calculate integral using contour integration. Complete explanation is required. integral(-&#8734;->+&#8734;)dx/(1+x^2)^n+1 keywords: integration, integrates, integrals, integrating, double, triple, multiple

    Contour Integrals

    Calculate the integral using contour integration. Complete explanation is required. integral(o->pi/2)d(theta)/(a+sin^2(theta)) keywords: integration, integrates, integrals, integrating, double, triple, multiple

    Contour Integrals

    Calculate the integral using contour integration. Complete explanation is required integral(o->&#8734;)(logx)^2dx/(1+x^2) keywords: integration, integrates, integrals, integrating, double, triple, multiple

    Contour Integrals

    Calculate the integral using contour integration. Complete explanation is required integral(o->&#8734;) dx/(x^3+1) keywords: integration, integrates, integrals, integrating, double, triple, multiple

    Taylor Polynomials and Partial Sums of Series

    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 &#8734; &#931; 1/(2p)&#8319; n=1 3 Calculate the sum of the first ten terms of the series, then estimate the error

    Trapezoid Reduction Formula

    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

    Romberg Integration Computing

    2 Use Romberg integration and compute A33 to approximate the integral &#8747; x ln x dx where m=3. Please show all work.

    Simpson's Rule and Composite Simpson's Rule and Errors

    (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.

    error in numerical integration

    See attached file for full problem description. Determine the values of n and h required to approximate the integral of xlnxdx in [1, 2] to within 10-5 and compute the approximation. a. Use composite Trapezoidal rule. b. Use the composite Simpson's rule. c. Use the composite Midpoint rule.

    Complex Integration : Holomorphisms

    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)

    Evaluating Integrals Presented

    Integrate the definite integral: |t|*e^-|t| from -infinity to infinity Is this a divergent or convergent integral and if the latter what is the answer?

    Ring of Integral Hamilton Quaternions and Isomorphisms

    Let I be the ring of integral Hamilton Quaternions and define N: I ->Z by N(a+bi+cj+dk) = a^2 +b^2 +c^2+d^2 a) Prove that N(k)= kk' for all k in I where if k=a+bi+cj+dk then k'=a-bi-cj-dk b)Prove that N(kr)=N(k) N(r) for all k,r in I c) Prove that an element of I is a unit iff it has norm +1. Show that I(with multiplicati

    Integration and substitution

    Integration 1. Given that express in terms of x. 2. Find using substitution u = 1-x2. Explain results geometrically. See attached file for full problem description.