A value of such that _ ^ +1 dx(x+ )(x+ +1)= _e ( 98 ) is:

Question

Accepted Answer

Correct answer: A. (a) JEEN Main 2019 dx(x+ )(x+ +1) = ( 1x+ - 1x+ +1) dx [Using partial fraction] = log ( ( (x+ )(x+ +1) ) )_ ^ +1= log ( 2 +12 +2 ∙ 2 +12 ) = log 98 (Given) So, (2 +1)^2 ( +1)= 92 ⇒8 ^2+8 +2=9 ^2+9 ⇒ ^2+ -2=0 ⇒ =1 ,-2

$A value of α such that \int_{α}^{α + 1} \frac{d x}{( x + α ) ( x + α + 1 )} = lo g_{e} (\frac{9}{8}) is:$

Solution

More Definite Integration PYQs