KCET · Maths · Definite Integration
The value of \(\int_{0}^{4}|x-1| d x\) is
- A \(\frac{5}{2}\)
- B 5
- C 4
- D 1
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \int_{0}^{4}|x-1| d x &=\int_{0}^{1}-(x-1) d x+\int_{1}^{4}(x-1) d x \\ &=-\left[\frac{x^{2}}{2}-x\right]_{0}^{1}+\left[\frac{x^{2}}{2}-x\right]_{1}^{4} \\ &=-[1 / 2-1]+[8-4-1 / 2+1] \\ &=-(-1 / 2)+(4+1 / 2) \\ &=1 / 2+9 / 2 \\ &=5 \end{aligned}\)
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