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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1
If [x][x] stands for the greatest integer function, the value of ∫410[x2][x2−28x+196]+[x2]dx\int\limits_{4}^{10} \frac{\left[x^2\right]}{\left[x^2-28 x+196\right]+\left[x^2\right]} d x, is
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Correct option: C
3
Option C (3) is correct because the integral is of the form ∫abf(x)f(x)+f(a+b−x)dx\int_a^b \frac{f(x)}{{f(x) + f(a+b-x)}} dx, which equals b−a2\frac{{b-a}}{{2}}.

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