Here,
I=int_1^4 (u-2)/sqrtuduI=∫41u−2√udu
=int_1^4 [u/sqrtu-2/sqrtu]du=∫41[u√u−2√u]du
=int_1^4 [sqrtu-2/sqrtu]du=∫41[√u−2√u]du
=int_1^4 [u^(1/2)-2u^(-1/2)]du=∫41[u12−2u−12]du
=[u^(1/2+1)/(1/2+1)-2xx(u^(-1/2+1))/(-1/2+1)]_1^4=[u12+112+1−2×u−12+1−12+1]41
=[u^(3/2)/(3/2)-2xxu^(1/2)/(1/2)]_1^4=[u3232−2×u1212]41
=[(4)^(3/2)/(3/2)-2xx(4)^(1/2)/(1/2)]-
[(1)^(3/2)/(3/2)-2xx(1)^(1/2)/(1/2)]=⎡⎣(4)3232−2×(4)1212⎤⎦−⎡⎣(1)3232−2×(1)1212⎤⎦
=[(2)^3/(3/2)-2xx2/(1/2)]-[1/(3/2)-2xx1/(1/2)]=[(2)332−2×212]−[132−2×112]
=[2/3xx8-8]-[2/3-4]=[23×8−8]−[23−4]
=16/3-8-2/3+4=163−8−23+4
=14/3-4=143−4
=2/3=23