Question:medium
Let \( f(x) = \int \frac{(2 - x^2) \cdot e^x \cdot \sqrt{1 + x} \cdot (1 - x)^{3/2}}{dx} \). If \( f(0) = 0 \), then \( f\left(\frac{1}{2}\right) \) is equal to:
Let \( f(x) = \int \frac{(2 - x^2) \cdot e^x \cdot \sqrt{1 + x} \cdot (1 - x)^{3/2}}{dx} \). If \( f(0) = 0 \), then \( f\left(\frac{1}{2}\right) \) is equal to:
Show Hint
Whenever you see \( e^x \) in an algebraic integral, immediately check if the remaining part can be split into a function and its derivative.
Updated On: Apr 2, 2026
- \( \sqrt{2e} - 1 \)
- \( \sqrt{3e} - 1 \)
- \( \sqrt{3e} + 1 \)
- \( \sqrt{2e} + 1 \)
Show Solution
The Correct Option is B
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