JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int\limits_4^{10} {\frac{{\left[ {{x^2}} \right]dx}}{{\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}}\) , where \(\left[ x \right]\) denotes the greatest integer less than or equal to \(x\), is
- A \(\frac{1}{3}\)
- B \(6\)
- C \(7\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(I = \int\limits_4^{10} {\frac{{\left[ {{x^2}} \right]}}{{\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} dx\).......\((1)\) \({\rm{Use}}\int\limits_a^b {f\left( {a + b - x} \right)} dx = \int\limits_a^b {f\left( x \right)dx} \)…
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