Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let a function f: R R be defined as f(x)=x+ x and I= ₀^ f⁻¹(x) d x then:

Options

AI> ₀^1 1 1+x^3 d x
BI < ₀^1 e^ x^2 d x
C2 < I < 3
D4 < I < 2

Correct answer

C. 2 < I < 3

Step-by-step solution

aligned & ₀^ f(x) d x+ ₀^ f⁻¹(x) d x= ^2 & and ₀^ f(x) d x= ₀^ (x+ x) d x= ( x^2 2 - x )₀^ = ^2 2 +2 & ( ^2 2 +2 )+ ₀^ f⁻¹(x) d x= ^2 aligned array ll & I= ^2 2 -2 & 2 < I < 3 & ₀^1 1 1+x^3 d x < ₀^1 1 d x < 1 < I array

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