Answered: In a vector field V = (y^a,−x^b,z^c)…

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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Verify Green 's theorem for the vector field F (x, y) = (x^2y, -xy^2) in the triangle OAB defined by the points O (0,0), A (1,0) and B (0.1).
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5) Integrate the vector field hla, y)= y2i+(2xy-ed4)J C t€ £0, 53. over the circular arc parumetrizal by P ltd= cost)ì + sinlt)s
Find a scalar field, 0, whose gradient is the irrotational vector V = (x² - yz, y² — xz, ² - xy) In other words, find such that Vo=V₁ Note: • Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful! • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, shift and - for subscripts, etc.) For multiplication, you can either leave a space, or use *. So x* x = xx = x². Note that this is not the same as x without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (Az. Ay, A₂) = {Az, Ay, A₂}. Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. o= (2A, 2A, 2A₂). + X .. 15 calc Opera Functi Symb Relati
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In a vector field V = (y^a,−x^b,z^c) what is the value of the z-component of curl (V) at (x, y, z) = (d, e, f) with a=3, b=4, c=4, d=1.2, e=0.3, f=2.9 ?