24bahut lamba hai yaar.........integration ki limits ko break kiya into 4 intervals.....[2][2] bekaar method hai......isliye koi acha method dhund raha hoon.....
\int_{0}^{1}({2x}-1)({3x}-1) dx=?????????
i got 19/72 after a long method..........half page[2][2]....
Whats ur answer........and plz post a shorte method if any
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24
39wohi toh general walla hain, then we have to wait. main bhii whaiin karta tha.
620∫1({2x}-1)({3x}-1) dx=
0∫1( {2x}{3x} - {3x} - {2x} + 1) dx
now in different parts..
then
{3x} will give 3.{1/2 x 1/3 x 1}=1/2
{2x} will give 2.{1/2 x 1/2 x 1}=1/2
1 will give area 1
{2x}{3x} is something that you have to work on..
that is a bit painful.. but to cut a long story short it will be
2x.3x from 0 to 1/3
2x{3x-1} from 1/3 to 1/2
(2x-1)(3x-1) from 1/2 to 2/3
(2x-1)(3x-2) from 2/3 to 1
this should not be that tough either!
24sir maine yehi to kiya hai..........[3][3]...main pooch raha tha ki koi aur shorter method hai kya?????
24theek hai............thanx for ur efforts......kuch mile to zaroor batana sir....