TS EAMCET · Maths · Definite Integration
If \([\cdot]\) denotes the greatest integer function, then \(\int_1^2\left[x^2\right] d x=\)
- A \(5+\sqrt{2}+\sqrt{3}\)
- B \(5+\sqrt{2}-\sqrt{3}\)
- C \(5-\sqrt{2}-\sqrt{3}\)
- D \(5-\sqrt{2}+\sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(5-\sqrt{2}-\sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(\int_1^2\left[x^2\right] d x = \int_1^{\sqrt{2}} 1 \, dx + \int_{\sqrt{2}}^{\sqrt{3}} 2 \, dx + \int_{\sqrt{3}}^2 3 \, dx\) \(= [x]_1^{\sqrt{2}} + [2x]_{\sqrt{2}}^{\sqrt{3}} + [3x]_{\sqrt{3}}^2\) \(= (\sqrt{2} - 1) + (2\sqrt{3} - 2\sqrt{2}) + (6 - 3\sqrt{3})\)…
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