IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

jessforyou

Pls post the method for integration folowing fns.

1.1/sqrt(sin³xsin(x+a))dx
2.limits pie/2 - pie

e^x[(1-sinx)/(1+cosx)]dx
3.limits 0 - pie

xtanx/(secx + tanx)

jessforyou

hellooo..??i need sum help here!!!

dheer_07

1 . expand sin[x+a] then take sin4 common out n u ii see cosec2 in num n cot in den now itz easy!!

2 write den as 2cos^2x\2 n separate ull get e^x sec^2 x\2 n e^x tanx\2 integrate by parts

3use p 5 n remone tanx frm numerator then convert into sin n cos n now its easy

hope u got it

plz rate for my efforts cheeeerrrs!!!!!!

jessforyou

hey u cant use p5 as the limits arent from zero

dheer_07

p5 mean int a to b f[x] = int a to b f [a+b-x]

jessforyou

Still u cant remove tanx

dheer_07

i didnt get it i mean use property n add it will be int 0 to pie tanx [ num] n secx + tanx[den]

now covert in sin n cos u ll get i= pie\2 int o to pie sinx[num]

n 1+ sinx in den

now solve hope u got it

raulrag009

Here the soln for Q3

$Let\\\\ I=\int_{0}^{\pi}{\frac{x\tan{x}}{\sec{x}+\tan{x}}}dx............(1)\\\\ Apply \;prop\\\\ I=\int_{0}^{\pi}{\frac{(\pi-x)\tan{x}}{\sec{x}+\tan{x}}}dx..............(1)\\\\ Add \;(1)\;and\;(2)\\\\ 2I=\pi\int_{0}^{\pi}{\frac{dx}{\sec{x}+\tan{x}}}\\\\ 2I=\pi\int_{0}^{\pi}{\frac{\cos{x}}{1+\sin{x}}}dx\\\\ Apply\;prop\\\\ 2I=2\pi\int_{0}^{\frac{\pi}{2}}{\frac{\cos{x}}{1+\sin{x}}}dx\\\\ Put\;\sin{x}=t\\\\ I=\pi\int_{0}^{1}{\frac{dt}{1+t}}\\\\ I=\pi\log{2}$

dheer_07

HEY RAUL I THINK U DID WRONG HOW CAN IT BE JUST 1/SECX+ TANX

CHECK 3 STEP PLZ!!

Nithy

3) multiply num denom (sec x - tan x)
denom is 1

then integrate secx tanx and tan^2 x as sec^x -1.

hope u get it........

1st Q asked so many ........ times here. do chk before posting

Nithy

2 split 1/cos x (f'(x) and -sinx/1+cos x (this is f(X)

use formula e^x f(X)

varshavallig

@nithy it is not secx-tanx ,it shud be secx+tanx then oly u will get denominator as 1.
then substitute sec^2x-1 for tan^2x.

3)see this link:
http://www.goiit.com/posts/list/integration-integration-problem-47004.htm
hope this helps
!!!!!!!!!

ramkumar_november

for the third sum..... go to this link.......

http://www.goiit.com/posts/list/integration-pls-tell-me-the-answers-47369.htm#235503

Nithy

@varsha.
what R u saying??? chk. denom secx+tanx MUST b secx-tanx
sec^2x -tan^2 x = 1.
its The simplest method. u'll get_{[ ]}

^{[ ]} secx tan x - _{[ ]}

^{[ ]} tan^2x. which is sec^2 x -1 ......................

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