CUET · MATHS · PYQ PAPER 2023
The value of the integral \(\int_1^3|x-2| d x\) is :
- A 2
- B 1
- C 4
- D 5
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
\(\int_1^3|x-2| dx = \int_1^2(2-x) dx + \int_2^3(x-2) dx\) \(= \left[2x - \frac{x^2}{2}\right]_1^2 + \left[\frac{x^2}{2} - 2x\right]_2^3\) \(= \left((4-2) - (2-0.5)\right) + \left((4.5-6) - (2-4)\right)\) \(= 0.5 + 0.5 = 1\)
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