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Proceeding from the definition, compute the following improper integrals (or prove their divergence): (a) int_(0)^(3a)(2xdx)/((x^(2)-a^(2))^(2//3)), (b) int_(0)^(2//pi)sin.(1)/(x)*(dx)/(x^(2)), (c ) int_(0)^(1)cos.(pi)/(1-x)*(dx)/((1-x)^(2)), (d) int_(2)^(6)(dx)/(sqrt((4-x)^(2))), (e ) int_(-1)^(-2)(dx)/(xsqrt(x^(2)-1)), (f) int_(1)^(2)(dx)/(x1n^(p)x) |
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Answer» (b) it DIVERGES; (C ) diverges; (d) `6root3(2);` (e ) `(PI)/(3);` (F) converges for `plt1` and diverges for `pge1`. |
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