Question

i need help on 47,49,61

45-74. Definite integrals Use a change of variables or Table 2.0 TO evaluate the following definite integrals.

Answer 1

GD Evaluate ( 22 (4x2) de Solution Testing the substitution 0-28 dn. da Differentiating with respect to the du = d (4-2) = 0.21 =)-2000 = du 7 landn=-dul limit of integration will be change accessingly tu= 4-1² at n=0, . u=4 - at n=1 . u=3 Then zu (4-22) dn = 1 = -13 udu 3-4429 -619-16) = 772 of anco-re) dm = 173Answers

Ji 2944 VI 2914 ③ Evaluate (3 21 de solution: Let I= . 13. 24 dn taking the substitution [u= 24 Differentialing with respect to se. e con ( 39-44) ale - 24 log (2) 40 du= 22 log (2), dn limit will be change accordingly e U= 2914 .. at nal, us 21+4=6 of a 3. u=2344 = 444 =12 is the limit of integration will be o [u= 6 to u=12] u12 Then 1320 dn= Ja 2*41 1.4 . du u tog (2)

logica du z [ Logouston Felgens Mag (12) - log69] hanging l bygg )] - logom pulang . = logem 1902) 34 (1 61 Evaluate la o te de solution : Taking the substitution -29 Po Diferentiating with respect to a () 32440 =) ou > 2n = ndr={du

er uanzel limit will be change accordingly at nzo, u= 0+1= 1 af =4, ua 43+1 = 16+1=17 ie the linist of integration is [u= 4. to 4:17] Then I am a du = 1 1 1 du = 1 1 1 1 1 de << Clogins, - - - I log(17) - loger] = ht log (17)-o - ** 2-83321. = 6.416607 pada = 1.416607 Answer Ho x² +1

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