NCERT Class 12 · Ch 7 Exercise 7.10 · Q18
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 18
Evaluate \(\int\limits_{0}^{4} \left|{x - 1}\right|\, dx\) using definite-integral properties.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(5\)
- Split the interval at x=1, where the expression inside the absolute value changes sign.
- Integrate the negative linear branch to the left and positive linear branch to the right, or add their triangular areas. The sum is \(5\).
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