AP EAMCET · Maths · Definite Integration
[.] represents a greatest integer function.If \(\int_{\sqrt{3}}^{\sqrt{18}}[x] d x=a+b \sqrt{2}+c \sqrt{3}\), then \(\mathrm{a}+\mathrm{b}+\mathrm{c}=\)
- A \(0\)
- B \(1\)
- C \(-1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\(\int_{\sqrt{3}}^{\sqrt{18}}[x] d x=\) \(\int_{\sqrt{3}}^{\sqrt{4}}[x] d x+\int_2^3[x] d x\) \(+\int_3^4[x] d x+\int_4^{\sqrt{18}}[x] d x\) \(=\int_{\sqrt{3}}^{\sqrt{4}} 1 d x+\int_2^3 2 d x+\) \(\int_3^4 3 d x+\int_4^{\sqrt{18}} 4 d x\) \(=(2-\sqrt{3})+(2)+(3)+4(\sqrt{18}-4)\)…
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