AP EAMCET2011MathematicsIndefinite Integration
( a+x a-x + a-x a+x ) d x is equal to
Options
- A2 ⁻¹ ( x a )+C
- B2 a ⁻¹ ( x a )+C
- C2 ⁻¹ ( x a )+C
- D2 a ⁻¹ ( x a )+C
Correct answer
B. 2 a ⁻¹ ( x a )+C
Step-by-step solution
aligned & Let I= ( a+x a-x + a-x a+x ) d x & Put x=a 2 d x=-2 a 2 d & I=- ( a+a 2 a-a 2 + a-a 2 a+a 2 ) & 2 a 2 d aligned aligned & =- ( 2 ^2 2 ^2 + 2 ^2 2 ^2 ) 2 a 2 d & =-2 a ( + ) 2 d & =-2 a 1 2 d & =-4 a d =-4 a +C₁ & =-2 a ⁻¹ ( x a )+C₁ & =-2 a [ 2 - ⁻¹ ( x a ) ]+C₁ & =2 a ⁻¹ ( x a )+C₁- a & =2 a ⁻¹ ( x a )+C, where C=C₁- a aligned