JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int \limits_{0}^{2} \| x-1|-x| d x\) is equal to
- A \(1.5\)
- B \(2.5\)
- C \(0.5\)
- D \(3.5\)
Answer & Solution
Correct Answer
(A) \(1.5\)
Step-by-step Solution
Detailed explanation
\(\int_{0}^{2}|x-1|-x \mid \mathrm{d} x\) Let \(f(x) \| x-1|-x|\) \(=\left\{\begin{array}{ll}1, & x \geq 1 \\ |1-2 x|, & x \leq 1\end{array}\right.\) \(A=\frac{1}{2}+1=\frac{3}{2}\) Or \(\int_{0}^{1 / 2}(1-2 x) d x+\int_{1 / 2}^{1}(2 x-1)+\int_{0}^{2} 1 d x\)…
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