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Teachers and Students => Universities => Topic started by: SGVaibhav on December 26, 2009, 03:18:28 pm

Title: INTEGRATION QUESTIONS!
Post by: SGVaibhav 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
Title: Re: INTEGRATION QUESTIONS!
Post by: XIII_BD 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!
Title: Re: INTEGRATION QUESTIONS!
Post by: SGVaibhav on February 12, 2010, 02:32:10 pm: np, thanks for help
i got it solved, when i asked this question in another thread.
Title: Re: INTEGRATION QUESTIONS!
Post by: SGVaibhav 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 :( :( :(
Title: Re: INTEGRATION QUESTIONS!
Post by: astarmathsandphysics on March 06, 2010, 12:29:13 pm: Half hour
Title: Re: INTEGRATION QUESTIONS!
Post by: astarmathsandphysics 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 $dx=sqrt{7/2}cos u$
$\int 1/sqrt(7-7sin^2 u) *sqrt{7/2}cosu du =\int 1/(sqrt{2}cosu) *cosu du =u=1/sqrt{2}*sqrt{2/7}sin^{-1} (x+1)+ C=sqrt{1/7}sin^{-1} (x+1)+ C$
Title: Re: INTEGRATION QUESTIONS!
Post by: SGVaibhav 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)..
Title: Re: INTEGRATION QUESTIONS!
Post by: astarmathsandphysics on March 06, 2010, 06:21:40 pm: One mo
Title: Re: INTEGRATION QUESTIONS!
Post by: astarmathsandphysics on March 06, 2010, 06:30:10 pm: http://www.astarmathsandphysics.com/a_level_maths_notes/C1/a_level_maths_notes_c1_completing_the_square_and_solving_quadratic_equations.html