4. What would be the best change of variables in the double integral which yields the simplest
form?

See attached.

Write the integral in the new variables and sketch the domain of integration for the new variables. Assume that f(x) is even, i.e. that f(-t)=f(t)

5. Compute the double integral of the function (see attached) over the upper semi-circle of radius r=1. Which coordinates are more suitable for this computation?

... of axioms for geometry, trigonometry, calculus and other ... we introduce coordinates and think about vectors, one can ... and angle in terms of vector operations, and ...

... electric field vector E, electric field vector points from ... I = dQ/dT (in the language of differential calculus). ... of (R1 + R2 + R3) since application of voltage ...

... chapter 12 and 15 discussion of stochastic calculus. ... thorough collection of such applications.) For many applications,. ... where θ is a vector of quality-adjusted ...

... Discussion of arthropod parasites and disease vectors. ... public health, epidemiology, vector biology, important ... analyses, matrix algebra, calculus, and computer ...

... where X ist is a vector of covariates including age ... and x and z are the vectors of socio ... actual transfer incomes have not been incorporated in poverty calculus. ...

... The way to multiply matrices by vectors is illustrated in ... matrix transforms an nx1 vector into an mx1 vector. ... By the fundamental theorem of Calculus 2 we know ...