Q32] evaluate the Cauchy principal value of the given improper integral.roo1dx6x + 25roo(x2 + 1)2 drroodr4)3dxLoo (x? + 1)*(x² + 9)(x2

The Cauchy principal values of the given improper integrals areevaluated as shown below.

Answered: evaluate the Cauchy principal value of…

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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Q/Find the Integral of the following: 2y y²-25 25- [x²√2x+1 dx dx dx 2x/Inx 3- J
Determine the indefinite integral. Check your work by differentiation. (5x3 - 8x + 2) dx O 15x4 - 16x? + 2x + C O 5x4 - 8x2 + 2x + c x+ - 4x² + 2x + C O 15x2 - 8 + C
et △ABC be a triangle in S^2 (the two-dimensional sphere). Let the dual point C'∈S^2 of C be defined by the following three conditions:(i) d(C' , A)=π/2(ii) d(C' , B)=π/2(iii) d(C' , C)≤π/2A' and B' are defined analogously. Thus we get a dual triangle △A' B' C'. More precisely, △ABC is a non-degenerate triangle, andit follows (you may assume) that △A' B' C' is too.(question) Are there triangles △ABC in S^2 identical to their own dual △A'B'C'? I would be very thankful if you could provide some explanation with the steps, thank you in advance.

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evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2 + 1)? roo (x2 + 4)3 dx -00 roo (x2 + 1) (x² + 9)