NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice
Let I 1 = ∫ 0 α 1 + 2 cos x 1 + e x d x and I 2 = ∫ 0 α 1 + e x 1 + 2 cos x d x , where α is the root of the equation 2 cos x - e x = 0 . Then,
Options
- AI 1 = I 2
- BI 1 > I 2
- CI 1 + I 2 = 0
- DI 1 < I 2
Correct answer
B. I 1 > I 2
Step-by-step solution
As, x ∈ 0 , α ⇒ 2 cos ⁡ x > e x ∴ 1 + 2 cos ⁡ x 1 + e x > 1 + e x 1 + 2 cos ⁡ x ⇒ ∫ 0 α 1 + 2 cos ⁡ x 1 + e x d x > ∫ 0 α 1 + e x 1 + 2 cos ⁡ x d x ⇒ I 1 > I 2 Also, I 1 , I 2 > 0