Question:medium
If \(f(x) = \frac{e^x}{1+e^x}, I_1 = \int_{-a}^a xg(x(1-x)) \, dx\) and \(I_2 = \int_{-a}^a g(x(1-x)) \, dx\), then the value of \(\frac{I_2}{I_1}\) is:
If \(f(x) = \frac{e^x}{1+e^x}, I_1 = \int_{-a}^a xg(x(1-x)) \, dx\) and \(I_2 = \int_{-a}^a g(x(1-x)) \, dx\), then the value of \(\frac{I_2}{I_1}\) is:
Show Hint
For integrals with symmetric integrands, pay attention to how the variable behaves. In cases with even symmetry, terms involving odd powers of the variable will cancel out.
Updated On: Nov 28, 2025
- -1
- -3
- 2
- 1
Top Questions on Integration
- If \( f(x) = \int_{0}^{\sin^2 x} \sin^{-1} \sqrt{t} \, dt \) and \( g(x) = \int_{0}^{\cos^2 x} \sin^{-1} \sqrt{t} \, dt \), then the value of \( f(x) + g(x) \) is:
- WBJEE - 2025
- Mathematics
- Integration
- Let \( f(x) = \max\{x + |x|, x - |x|, x - [x]\} \), where \( [x] \) stands for the greatest integer not greater than \( x \). Then \( \int_{-3}^{3} f(x) \, dx \) has the value:
- WBJEE - 2025
- Mathematics
- Integration
- Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
- MHT CET - 2025
- Mathematics
- Integration
- Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
- MHT CET - 2025
- Mathematics
- Integration
- Want to practice more? Try solving extra ecology questions todayView All Questions