IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

faizameer

Hey....guyz

I think most of 12th std students will have difficulty in integration.

So letz start a game...,a game in integration.

I will give a problem in integration. Those who solve it should write another problem and so on.

*Those who submit problems should try to give standard problems.

(*)And finally we can decide who is the king in Integration........................

faizameer

Integrate

sin^2(x) dx/(cosx+sinx)

*limits given 0 to pi/2

So......on your mark...set.... go

ankit7465

I = sin^2(X) dx / (sinx + cosx)
use the property...
I = cos^2(X) dx / (sinx +cosx)
then add them..:
2I = dx / (sinx + cosx)
then mult. n div. by root 2 in denomeinator and then solve it...

ankit7465

now my question...

1) integrate e^1/x dx
or
2) integrate e^x.logx dx

faizameer

One more thing......If U think that the method of solution for the problem that you have posted is different from that of the answered,U can explain ur own method.....Letz master in integration..........

faizameer

So.... My method of solving the problem that I have posted is

after getting 1/sinx+cosx

Put t = tan x/2

then..., dx=2dt/1+t^2

sinx=2t/1+t^2

cosx=1-t^2/1+t^2

Substitue...and integrate using any standerd formula

Hope u got it

faizameer

Now proceed with ankit7465's Problem................

faizameer

You can rate those who give the perfect answer....I have rated you..ankit7465

mrids_11

ankit both r non-integrable

my question---

(sin^-1

x - cos^-1

x)/ (sin^-1

x + cos^-1

x)

dis is ncert question no. 19 misc ex(pg 352)

faizameer

mrids_11

wat was blank post for?

sboosy

for the previous question denominator is

/2

so take 2/

common

cos^-1x=

/2-sin^-1x

so we get numerator in terms of sin^-1x

put

x=t and hence the problem

hsbhatt

Find ₀

^/2 sin²(sinx) + cos²(cosx) dx

sboosy

split it into 2 integrals as I and J
for I that is sin^ 2 (sinx)
apply property 4
u get I as sin^2 (cosx)
now add new I and old J
so pi/2
correct me if i m wrong

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