AP EAMCET201823 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual
d x x+ x+ x+ cosec x =
Options
- A1 2 ( x- x+x)+c
- B1 2 ( x- x- x+ x)+c
- C1 2 ( x- x-x)+c
- D1 2 ( x+ x- x- x)+c
Correct answer
C. 1 2 ( x- x-x)+c
Step-by-step solution
We have, aligned & d x x+ x+ x+ cosec x = & d x x x + x x + 1 x + 1 x = & x x d x ^2 x+ ^2 x+ x+ x = & x x d x 1+ x+ x aligned multiply and divide by 2 aligned & = 1 2 2 x x 1+ x+ x d x & = 1 2 2 x x+1-1 1+ x+ x d x & = 1 2 ( ^2 x+ ^2 x+2 x x )-1 1+ x+ x d x & = 1 2 ( x+ x)^2-1 1+ x+ x d x & = 1 2 ( x+ x+1)( x+ x-1) 1+ x+ x d x & = 1 2 ( x+ x-1) d x & = 1 2 [- x+ x-x]+c & = 1 2 [ x- x-x]+c aligned