NDA2021MathematicsIndefinite IntegrationActual
If 1- 2 x d x=A x+B x+C , where 0 x 4 , then which one of the following is correct?
Options
- AA+B=0
- BA+B-2=0
- CA+B+2=0
- DA+B-1=0
Correct answer
A. A+B=0
Step-by-step solution
aligned & I = 1- ^2 x d x, 0 x 4 & = ^2 x-2 x x+ ^2 x d x & = ( x- x)^2 d x aligned (i.e. x- x 0 when 0 x 4 ) aligned & I =- ( x- x) d x= ( x- x) d x & I = x- x+c= A x+ B x+ c aligned Thus, A+B=1-1=0