Question

Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 1+1 61 +2= convergent divergent

please show work?

Answer 1

61X (m?+2n) can abo be written as z thi lim 61 X (n+1) da which tyd m2+2n) to get integral value we have to substituti tas D which will be the uestion given. means q Now t t lim tyo Sci xona x mil) da (n²+2n) lim 618 tD (n+1) da Jon'721) San Now t lim Glx n²+2n = n(n+2) hence is Carl) an lim 61X 2. (2+1) dx 2 (7+2) tyd 1 (m +2n) to None (2) + (n+2) anta 2(a+] N

N 2 2 hence (a) + (n+3) 2 (nt) (1+) (0) + Cate) 를 substituting this in the equation given (2) + (mt2) du lim 2 (a) (ntz) t t lim 61X 61X (at du n(n+2) مدا tyd - t which implies lim 61x (2) + (at2) da 2 teda 1 n (ntz) t 61X + lim to SH 1 (2+2) dx (2) + (n+2) Z 1 + 1 (2+2) dividing separately n n (at2) we know Sau In (at2) 2 (2+2) and St 2 these substituting / 2 Values he get

lim 61 x du Sante n Intl t>D L lim toa 61 x In (n+ 2) + lux ( 1 (1) 400 2. applying upper limit and lower limit GIX lim >> In (t+2) + Inft) - [In C1tz] + lac ty in (1) 2 In (t + 2) + lu(t) tim ta २ 2. In(a)t ln (b) 2 In Cab 14645] - loc). In ale] = 2 Glx inlttal tz D how putting 2 to u z) 61 x In Lo hence then integral is diversent . 리 2

to a output / thes 8V value as a finite Af the integral value a finito integral conyeeges gives it is convergent, if it gives an infinite value as output it is divergent. (like' please leave a if you are happy with the answer