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    Integrals

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    Partial Derivative and Double Integral

    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

    Revolution of integrals - asteroids

    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)

    Revolutions of integrals - torus

    The circle x=acost, y=asint, 0≦t≦2pi is revolved about the line x=b, 0<a<b, thus generating a torus (doughnut). Find its surface area. Area if the torus:_____________.

    Rotation of Solid Integrals

    Find the volume of a solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse *See attached for equation* and the x-axis and thus find the volume of a prolate spheroid. Here a and b are positive constants, with a<b Volume of the solid of revolution: Please see attachment for det

    Volume of a Solid Integration

    See attached for Diagram The base of a certain solid is the area bounded above by the graph of y=f(x)=16 and below by the graph of y=(gx=36*. Cross sections perpendicular to the x-axis are squares. See picture above. Use formula (see attachment) to find the volume of the solid.

    Evaluating integrals

    Evaluate the integral from 0 to infinity of (e^(-at) - e^(-bt))/t dt for a,b > 0

    Integration - Volume of Rotation

    Find the volume of the solid obtained by rotating the region bounded by the given curves: y=1/x^6, y=0, x=4, x=8 about the "y" axis

    Volume of a Solid of Rotation

    Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by: y= x^4 y= 125x about the x-axis. I am more concerned with understanding than the answer. Thanks for your help.

    Evaluate the integral

    The following expression describes the total electric current to pass in the circuit please see attached

    Find the area between the curves

    Find the area between the curves y = x2 + x + 1 and y = 2x + 7 From x = -2 to x = 3 Sketch the curve and indicate the interval and the enclosed area

    Integral domain

    There is integral domain with exactly six elements. Disprove or Prove

    Acceleration and Velocity

    An object is thrown downward from the top of a building with an initial velocity of 30 m/s. Assuming a positive direction of y measured downward from the top, derive an expression for (a) the velocity and (b) the displacement as a function of time. Assume y(0)=0

    MATLAB Programming

    Develop a program (M-File) called 'integrate' that will perform a first-order numerical approximation, yi(t), of the running integral with respect to time of an array of experimental data y(t). The M-File must also perform another first order approximation, yi2(t), of the first integral resulting in a double integration of the

    Evaluate the Surface Integral

    Please see the attached file for the fully formatted problems. Evaluate the surface integral SSs x dS, where S is part of the plane x = 2y = 3z = 6 that lies in the first octant.

    Green's Theorem : Evaluating a Line Integral

    Please see the attached file for the fully formatted problems. Use Green's Theorem to evaluate the line integral Sc xy dx +x^2y^3 dy where C is the triangle with vertices (0,0), (2,0) and (2,2).

    Gradients : Find a Function and Evaluate an Integral

    Please see the attached file for the fully formatted problems. (a) Find a function f so that grad(f) = yi + (x + 3y^2)j (b) Use part (a) to evaluate Sc grad(f) dt where C is the path starting at (0,2) goes down the y-axis to (0,0), along the x-axis to (2,0).