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Author Topic: INTEGRATION QUESTIONS!  (Read 2307 times)

Offline SGVaibhav

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INTEGRATION QUESTIONS!
« on: December 26, 2009, 03:18:28 pm »
Guys i have many doubts in integration
i will not be posting them, because they r quite long, so leave those.

now i will put a small doubt that i have.

im posting it in a pic


i do not understand how does the number which comes out is 2??
the number which comes out is supposed to be 4 actually ???

the stuff  // steps i have written is 100 % correct ...

HOW HOW HOW ???

please help fast, because i have a test coming up, and this concept will affect the stuff i learn after this
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Offline XIII_BD

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Re: INTEGRATION QUESTIONS!
« Reply #1 on: February 12, 2010, 01:08:24 pm »
well u cn take 4 common frm within the square root out! root over 4 means 2. and there is no integration of 2. so it goes outside the integration sign!
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Offline SGVaibhav

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Re: INTEGRATION QUESTIONS!
« Reply #2 on: February 12, 2010, 02:32:10 pm »
np, thanks  for help
i got it solved, when i asked this question in another thread.
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Offline SGVaibhav

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Re: INTEGRATION QUESTIONS!
« Reply #3 on: March 06, 2010, 11:58:32 am »
Help me to integrate this question

\int 1/sqrt(5-4 x-2 x^2) dx

It was solved in our class by completing the sqaure, but i did not understand :( :( :(
« Last Edit: March 06, 2010, 12:02:09 pm by sgvaibhav »
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Offline astarmathsandphysics

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Re: INTEGRATION QUESTIONS!
« Reply #4 on: March 06, 2010, 12:29:13 pm »
Half hour
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Offline astarmathsandphysics

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Re: INTEGRATION QUESTIONS!
« Reply #5 on: March 06, 2010, 01:21:27 pm »
\int 1/sqrt(5-4 x-2 x^2) dx

5-4 x-2 x^2=b-c(x+a)^2 =b-cx^2-2acx-ca^2
from which
c=2
-4x=-2cax so a=1
5=b-ca^2 so b=5+2*1^2=7
\int 1/sqrt(7-2(x+1)^2 dx
sub x+1=sqrt{7/2}sin u so dx=sqrt{7/2}cos u
\int 1/sqrt(7-7sin^2 u) *sqrt{7/2}cosu du =\int 1/(sqrt{2}cosu) *cosu du =u=1/sqrt{2}*sqrt{2/7}sin^{-1} (x+1)+ C=sqrt{1/7}sin^{-1} (x+1)+ C
« Last Edit: March 06, 2010, 01:30:13 pm by astarmathsandphysics »
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Offline SGVaibhav

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Re: INTEGRATION QUESTIONS!
« Reply #6 on: March 06, 2010, 02:59:10 pm »
how can it be done by this method

The final answer is not important....

once i get into the integral, i can solve it by trigonometric substitution...

but i dont understand the completing the sqaure thing   (i asked the same thing in the other thread also... no need to reply in both, reply in any one)..
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Offline astarmathsandphysics

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Re: INTEGRATION QUESTIONS!
« Reply #7 on: March 06, 2010, 06:21:40 pm »
One mo
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Offline astarmathsandphysics

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Re: INTEGRATION QUESTIONS!
« Reply #8 on: March 06, 2010, 06:30:10 pm »
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