If _0^1 0.05em 1 3+x+ 1+x dx=a+b 2+c 3, where a ,b ,c are rational numbers, then 2a+3b-4c is equal to :

Question

Accepted Answer

Correct answer: D. (d) _0^1 0.05em 1 3+x+ 1+x dx= _0^1 0.05em 3+x- 1+x (3+x )- (1+x ) dx 12( _0^1 0.05em 3+x dx- _0^1 ( 1+x ) dx) 12(2 (3+x )^ 323- 2 (1+x )^ 323)_0^1 12( 23 (8-3 3 )- 23(2^ 32-1)) 13 [8-3 3-2 2+1 ] =3- 3- 23 2=a+b 2+c 3a=3 ,b=- 23 ,c=-12a+3b-4c=6-2+4=8

$If \int_{0}^{1} \frac{1}{3 + x + 1 + x} dx = a + b 2 + c 3, where a, b, c are rational numbers, then 2 a + 3 b - 4 c is equal to :$

Solution

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