AP EAMCET202123 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual
x- x 2 x d x is equal to
Options
- A- | x- x+ 2 x |+C
- B- | x+ x- 2 x |+C
- C- | x+ x+ 2 x |+C
- D- | x- x- 2 x |+C
Correct answer
C. - | x+ x+ 2 x |+C
Step-by-step solution
Let I= x- x 2 x d x aligned & I= x- x 1+2 x x-1 d x & I= x- x ( x+ x)^2-1 d x aligned Let x+ x=t array lr & x- x= d t d x & -( x- x) d x=d t & ( x- x) d x=-d t array I=- d t t^2-1 [ 1 x^2-a^2 d x= |x+ x^2-a^2 |+C ] aligned & =- |t+ t^2-1 | & =- | x+ x+ ( x+ x)^2 -1 |+C & I=- | x+ x+ 2 x |+C aligned