IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

v_gurucharan

INTEGRATE

1/(X+X^1/2) LIMITS 0 TO 4

bhuwanaroracorroded

in denominator take out foot x common

seperate by partial fraction

4 rootx +1 let rotx=t

then solve

v_gurucharan

SRY,VERY DIFF. TO UNDERSTAND WHAT U MEAN!!!
ANY ONE ELSE COMMEON!!!

hsbhatt

1(x+

x) = 1/

x(1+

x)

Now let

x = t. Then dx/2

x = dt

Thus our integral becomes 2

dt/(1+t)

mrids_11

_{[0 ]}

^{[ 4]} 1/(x+x^1/2)

=_{[0 ]}

^{[4 ]} 1/x^1/2(x^1/2+1)

now let x^1/2=t

so 1/2x^1/2dx=dt so lim will b frm 0 to 2

=_{[0 ]}

^{[ 2]} 2dt/(t+1)

=2 log t+1] 0 to 2

=2log3/1 =2log 3