Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration
Paragraph: If equation of column-I is given along with condition of column-II then match it with appropriate value given in column-III. Question: Which of the following is incorrect combination?
Options
- A(II) (i) (Q)
- B(I) (iii) (R)
- C(II) (ii) (Q)
- D(I) (ii) (P)
Correct answer
C. (II) (ii) (Q)
Step-by-step solution
(I) ₀^2 f(x) d x= ₀^1 f(x) d x+ ₁^2 f(x) d x Let x=2 t d x=2 d t 2 ₀^1 f(2 t) d t=I+ ₁^2 f(x) d x If f(2 x)=3 f(x) then ₁^2 f(x) d x=5 (I) (ii) (P) and also (II) ₀^4 f(x) d x= ₀^2 f(x) d x+ ₂^4 f(x) d x Let x=2 t 2 ₀^2 f(2 t) d t=2+ ₂^4 f(x) d x If f(2 x)=2 f(x) then ₂^4 f(x) d x=6 (II) (i) (Q) and ₀^3 f(x) d x= ₀^1 f(x) d x+ ₁^3 f(x) d x Let x=3 t 3 ₀^1 f(3 t) d t=1+ ₁^3 f(x) d x If f(3 t)=3 f(t) then ^3 f(x) d x=8 (I) (iii) (R) and ₀^9 f(x) d x= ₀^3 f(x) d x+ ₃^9 f(x) d x Let x=3 t 3 ₀^3 f(3 t) d t= ₀^3 f(x) d x+