WBJEE · Maths · Definite Integration
Let \(f(x)\) denotes the fractional part of a real number \(x\). Then, the value of \(\int_{0}^{\sqrt{3}} f\left(x^{2}\right) d x\) is
- A \(2 \sqrt{3}-\sqrt{2}-1\)
- B 0
- C \(\sqrt{2}-\sqrt{3}+1\)
- D \(\sqrt{3}-\sqrt{2}+1\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2}-\sqrt{3}+1\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_{0}^{\sqrt{3}} f\left(x^{2}\right) d x=\int_{0}^{\sqrt{3}}\left\{x^{2}\right\} d x\) \(\left.=\int_{0}^{\sqrt{3}}\left(x^{2}-\mid x^{2}\right)\right) d x\) \(=\int_{0}^{\sqrt{3}} x^{2} d x-\int_{0}^{\sqrt{3}}\left|x^{2}\right| d x\)…
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