Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration
If f(x)= | array ccc 4 ^2 x & 1 & 1 (1- x)^2 & (2+ x)^2 & (1- x)^2 (1+ x)^2 & (1+ x)^2 & ^2 x array | , then evaluate _ - / 2 ^ / 2 f(x) d x -
Correct answer
4
Step-by-step solution
Applying C₁ C₁-C₃ and C₂ C₂-C₃ , we get aligned & f(x)= | array ccc 4 ^2 x-1 & 0 & 1 0 & 3(2 x+1) & (1- x)^2 (2 x+1) & (2 x+1) & ^2 x array | & =(2 x+1)^2 | array ccc 2 x-1 & 0 & 1 0 & 3 & (1- x)^2 1 & 1 & ^2 x array | & =-16 ^3 x ^2 x-24 ^2 x ^2 x-12 x ^2 x-2 ^2 x & & = _ - / 2 ^ / 2 f(x) d x & = _ - / 2 ^ / 2 (-24 ^2 x ^2 x-2 ^2 x ) d x=-4 aligned