Question

If $[x]$ stands for the greatest integer function, the value of $\underset{4}{\overset{10}{\int }}\frac{\left[x^2\right]}{\left[x^2-28x+196\right]+\left[x^2\right]}dx$ is :

• A. 0
• B. 1
• C. $3$
• D. $\frac{3}{2}$

Answer 1

Answer: (C)

$I=\underset{4}{\overset{10}{\int }}\frac{\left[(x-14{)}^2\right]}{\left[x^2\right]+[(x-14{)}^2}dx$
$\Rightarrow 2I=\underset{4}{\overset{10}{\int }}dx=6\Rightarrow I=3$