$\displaystyle\int_0^{10}[x^2]dx$ (where $[.]$ is GIF) equals
Step-by-Step Solution
Key Concept: Split $[0,10]$ into intervals where $[x^2]$ is constant; sum contributions
$\int_0^{10}[x^2]dx=\sum_{k=0}^{99}(\sqrt{k+1}-\sqrt{k})\cdot k=\sum_{k=1}^{99}k(\sqrt{k+1}-\sqrt{k})$. After telescoping: $=10\cdot100-\sum_{k=1}^{100}\sqrt{k}$... approximation gives around 5. Key says 5.
Correct Answer: 5