JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \([t]\) denote the greatest integer function. If \(\int \limits_0^{2.4}\left[x^2\right] d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}\), then \(\alpha+\beta+\gamma+\) \(\delta\) is equal to \(..............\).
- A \(6\)
- B \(5\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(\int \limits_0^1 0 dx +\int \limits_1^{\sqrt{2}} 1 dx +\int \limits_{\sqrt{2}}^{\sqrt{3}} 2 dv +\int \limits_{\sqrt{3}}^2 3 dx +\int \limits_2^{\sqrt{5}} 4 dx +\int \limits_{\sqrt{5}}^{2 \cdot 4} 5 dx\)…
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