WBJEE · Maths · Definite Integration
\(\int_0^{1.5}\left[x^2\right] d x\) is equal to
- A \(2\)
- B \(2-\sqrt{2}\)
- C \(2+\sqrt{2}\)
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(2-\sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \int_0^{1.5}\left[x^2\right] d x \\ & =\int_0^1\left[x^2\right] d x+\int_1^{\sqrt{2}}\left[x^2\right] d x+\int_{\sqrt{2}}^{3 / 2}\left[x^2\right] d x \\ & =0+1(\sqrt{2}-1)+2(1.5-\sqrt{2}) \\ & =2-\sqrt{2}\end{aligned}\)
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