KCET2009MathematicsDefinite Integration
If f(x)= _ -1 ^ x |t| d t , then for any x 0, f(x) is equal to
Options
- A1- x ²
- B1 2 (1+ x ² )
- C1+x²
- D1 2 (1- x ² )
Correct answer
B. 1 2 (1+ x ² )
Step-by-step solution
Given, f ( x )= _ -1 ^ x | t | dt aligned &= _ -1 ⁰| t | dt + ₀^ x | t | dt &= _ -1 ⁰- t dt + ₀^ x t dt &=- [ t ² 2 ]_ -1 ⁰+ [ t ² 2 ]₀^ x =- [0- 1 2 ]+ [ x ² 2 -0 ] &= 1 2 (1+ x ² ) aligned