65–68. Improper integrals Improper integrals arise in polar coordi-nates when the radial coordinate r becomes arbitrarily large. Undercertain conditions, these integrals are treated in the usual way:[B[B (b(r. 0) r dr do = lim e(r. 0) r dr do.bUse this technique to evaluate the following integrals.dARis the first quadrant.(1 + x? + y?)²*

To Evaluate: ∬R11+x2+y22dA, using polar coordinates and taking r as arbitrarily large.

Answered: 65–68. Improper integrals Improper…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(1) Consider the following: x = 1+t-1 and y = t2. Express in the form y = f(x) by eliminating the parameter. (2) Find the arc length of the curve c(t) = (x(t),y(t)) = (sin(3t), cos(3t)) for 0 les or equal to t and less or equal to π (3) Express the Cartesian coordinate (2, 3) in polar coordinates in at least three different ways (4) Consider the four petaled rose r = sin(2θ). Find the area of one leaf, then prove that the total area of the rose is equal toone-half the area of the circumscribed circle.
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