Question

Evaluate the improper integral or show that it is divergent. dc r2 + 4 S. 22 (22 + 4) da Loitzada dan poo Jo 1 + x2 1 1 + 9x2 dx

Answer 1

integral is Given improper 00 de fra = I x (the) J x²(x²+2) Compare it by function in stea de is endetined at the upper linit The 200 Let - 24 gex) = fim fen) tim zate) = no o ana x ats gcn) No i tim nyo fin) & 1 to 9(2) ? By limit comparison test both the integrals I fenn du and IgG) da converge or dirage together But we know that I do is convergen iff nyl. so, o ay is convagent. This i tenistanis convergent Hence the improper interat att din is o , convergents by limit companson test.

Given improper intyral is 92 is the only point of Here the upper limit infinite dis continety. are know that sa dx = h 2 tan (2). 1tan2 = ( tani (3x) – tanca Him [taal (on- 9] tanloy = 0 | - tonks-o - Į tan'(o) tan II = 0 tenilor The value of Hence the interal is the given list and tinite improper integral is Convergent.

consida the improper intged is dn = him feas de + تلد لا ou Myot s I = fim dy Itaz tasot log (fea)] to tem 20 dx Itxe fons >-00 log (14x²) - - اعع fo de cent ((5+ au) – log (14x2] 3.0 19 I tim lo Mtot A -s The limit the improped does not integral enest. does not Thes convyes. -de in diverges. tx²