Question:medium
Let \( f(x) \) be differentiable and
\[ \int_{0}^{t^2} x f(x)\,dx = \frac{1}{2} t^4 \quad \text{for all } t. \]
Then the value of \( f(17) \) is ______.
Let \( f(x) \) be differentiable and
\[ \int_{0}^{t^2} x f(x)\,dx = \frac{1}{2} t^4 \quad \text{for all } t. \]
Then the value of \( f(17) \) is ______.
Show Hint
Always multiply by derivative of upper limit when differentiating integrals.
Updated On: Apr 30, 2026
- \(17\)
- \(1\)
- \(1/17\)
- \(17/2\)
- \(19\)
Show Solution
The Correct Option is B
Solution and Explanation
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