99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration
If I 1 = ∫ 0 1 2 x 2 d x , I 2 = ∫ 0 1 2 x 3 d x , I 3 = ∫ 1 2 2 x 2 d x and I 4 = ∫ 1 2 2 x 3 d x , then
Options
- AI 3   >   I 4
- BI 3   =   I 4
- CI 1   >   I 2
- DI 2   >   I 1
Correct answer
C. I 1   >   I 2
Step-by-step solution
Given that, I 1 = ∫ 0 1 2 x 2 d x ,   I 2 = ∫ 0 1 2 x 3 d x ,   I 3 = ∫ 1 2 2 x 2 d x and I 4 = ∫ 1 2 2 x 3 d x From the graph it is clear that ∵   2 x 3 < 2 x 2 ,   0 < x < 1 and 2 x 3 > 2 x 2 ,   x > 1 ∴   I 4 > I 3 and I 2 < I 1