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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let f: R R defined by f(x)= x+x if ₀^ f⁻¹(x) d x= ^2 2 -k , then the value of k is

Correct answer

2

Step-by-step solution

₀^ f⁻¹(x) d x= ₀^ t f^ (t) d t aligned & =[t f(t)]₀^ - ₀^ (t+ t) d t & = ^2- ^2 2 -1-1 & = ^2 2 -2 & k=2 aligned

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