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Q.
If $[x]$ stands for the greatest integer function, the value of $\int\limits_4^{10} \frac{\left[x^2\right]}{\left[x^2-28 x+196\right]+\left[x^2\right]} d x$ is :
Integrals
Solution:
$I=\int\limits_4^{10} \frac{\left[(x-14)^2\right]}{\left[x^2\right]+\left[(x-14)^2\right.} d x$
$\Rightarrow 2 I=\int\limits_4^{10} d x=6 \Rightarrow I=3$