IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

kghedriu

Hi dear goiitians.....

m Goutham.....just entered into class 12...and in our board syllabus, we dont hav integral calculus in 11th....

now in 12th, our math lecturer is in a hurry of completing the entire portion by november....

so, he is dealing integral calculus with a great speed.....

he is presently teaching indefinite integration....he is just giving the formulae and working out all sums for himself....

m not at all able to solve even 50% of the sums.....evrysum appears as a big hurdle.....he uses methods in his solns tht appear wierd to all of us(our classmates).....

m facing heavy trouble.....

pls help me out in telling some tips that help in solving sums related to this chapter...i will b greatful to all of u....

pls pls help me...

Thank u..

with regards..

Goutham Harsha

vasanth

there are four methods

1) decomposition into sum or product -------for trigonometric fn

2) integration by parts-------when the expression is a product of 2 terms

3) substitution

4) formulae

plzzz rate me

i'm ready to explain any of the above topics

plzz ask which u want

cheeeeers

vasanth

i'm postin a few formulae.......

i'm asuuming that u kno the basic formulae

1)when trig fn are given u reduce them to the sum or difference of trigo fn....

fro ex: (1- cosx)/(1+cosx) can be reduced to

2cosec²x - 2 cosecx cotx -1 which can b easily integrated

2)INTEGRATION BY PARTS(very important)

u dv = uv -

v du

it's success depends upon the choice of u

(1) if integrand contains any non integrable functions directly from the formula, like tan^-1x, logx we have to take these non integrable functions as u and the other as dv.

(2) if integrand contains both integrable functions, and one of these is xⁿ ( n is positive integer). then we take u=xⁿ .

(3) for other cases choice of u is yours

cheers

vasanth

i'm posting certain standard integrals

(a² - x²) dx = (x/2)(

(a² - x²) + (a²/2)sin^-1(x/a) + c

(x² - a²) dx = (x/2)(

(x² - a²) - (a²/2)log[x +

(x² - a²)] + c

(x² + a²) dx = (x/2)(

(x² + a²) + (a²/2)log[x +

(x² + a²)] + c

dx/[

(a² - x²) = sin^-1(x/a) +c

dx/[

(x² - a²) = log[x+

(x² - a²)] + c

dx/[

(x² + a²) = log[x+

(x² + a²)] + c

dx/(a² - x²) = (1/2a)log [ (a+x)/(a-x)] + c

dx/(x² - a²) = (1/2a)log [ (x-a)/(x+a)] + c

dx/(x² + a²) = (1/a)tan^-1(x/a) + c

(e^ax sin bx ) dx = [e^ax/a² + b²][a sinbx - bcosbx] + c

a^xdx = a^x/log_ea + c

f '(x)/f(x) dx = log[f(x)] + c

f ' (x) /

f(x) dx = 2^*

f(x) + c

hope this helps....if u want the proofs i can mail them

plz rate if rite

cheeeeers

KAB

Hey goutham,
Integration is one of the most interesting chapter in maths.Start solving simpler problems first.Once you get the grip over the subject then go for tougher ones.

One must be thorough with the techniques involved in solving a problem.Some problems seem difficult but just by one proper substitution the problem can be easily solved.

All I can say is keep practising problems and NEVER EVER THINK THIS CHAPTER IS DIFFICULT.

You will soon enjoy integration!

chimanshu_007

hi goutham

don't get lost in the formulas

Integration as said above is most interesting chapter..... (and easy also i think)

there are jst some methods to b used

and integration is not a chapter which u willl forget
and u wanna get 1st rank in 2008 so u must strngthen ur calculas too
jst think "INTEGRATION IS NOTHING IN FRNT OF ME" use all above formulas (almost all are given) to solve qs

best of luck frnd

kghedriu

Thanxx himanshu, KAB and vasanth.....

nd evryone...pls mail ne thing regarding tackling of this chapter...pls...

i need ur help....

thank u..

Goutham

KAB

This is a very helpful link http://integrals.wolfram.com/index.jsp

Arjun

don worry about integration ,dude,

try solvin wid da simplest first!!!!!!

try usin R.S.AGGARWAL,

der r a hoard of simple problms and example,use it only for calculus!!!!!

if u think u can do it ,u really will do it!!!

integration is jus da reverse process of differntiation,
juss remember dis, den u can derive alotta simple formulae jus in ur mind!!!!

thanku!

cheer up!!!!!!

magiclko

hey gautham, try out the book for calculus by "I A Maron", everything about jee's calculus is thr in that (ofcourse many other things too, which u'll have to ignore)...... and if then also u are having any problems, we are here to solve it..... and its really an interesting chapter..... u'll love it to do, once u get in rhythm with it.... and start frm simple sums... not too high problems!!!

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