The value of \(\int_{1}^{3}\displaystyle |2x-1|\,dx\) equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
The expression \(2x - 1\) changes sign only at \(x = \frac{1}{2}\), which lies outside [1, 3]. For \(1 \le x \le 3\), \(2x - 1 \ge 1 \gt 0\), so the modulus can simply be removed:
\( \displaystyle \int_{1}^{3} |2x-1|\,dx = \int_{1}^{3} (2x-1)\,dx \)
\( \displaystyle = \Big[x^2 - x\Big]_{1}^{3} \)
\(= (9 - 3) - (1 - 1) = 6\)