IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

fwks_phoenix

I have a doubt in integration:

when we have to integregrate a division..can we integrate the denominator n numerator separately n get the answer??

for eg:

^{(cosx) / (sinx)}

in this case, is the answer

cosx /

sinx ??

dream_iit

no u cant , u have to either make it a single numerator or u can use partial fractions......

dream_iit

or either by substitution

sinx = t , cosx dx = dt

log |sinx| + C

fwks_phoenix

thanks

ashgirl

no, u cant coz

cosx/sinx = cot x and its integration is log|sinx| +c

and if u do individually then

integration of cosx is sinx

and integration of sinx is -cos x......

therefore overall is sinx/-cosx = -tanx

so u cant do denominator and numerator individually