JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region \(A=\{(x, y):(x-1)[x] \leq y \leq 2 \sqrt{x}, 0 \leq x \leq 2\}\) where \([t]\) denotes the greatest integer function, is
- A \(\frac{8}{3} \sqrt{2}-\frac{1}{2}\)
- B \(\frac{8}{3} \sqrt{2}-1\)
- C \(\frac{4}{3} \sqrt{2}-\frac{1}{2}\)
- D \(\frac{4}{3} \sqrt{2}+1\)
Answer & Solution
Correct Answer
(A) \(\frac{8}{3} \sqrt{2}-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(( x -1)[ x ] \leq y \leq 2 \sqrt{ x }, \quad 0 \leq x \leq 2\) Draw \(y =2 \sqrt{ x } \Rightarrow y ^{2}=4 x \quad x \geq 0\) \(y =( x -1)[ x ]=\left\{\begin{array}{c}0 \quad, 0 \leq x <1 \\ x -1,1 \leq x <2 \\ 2, \quad x =2\end{array}\right.\)…
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