A) 1
B) 2
C) 4
D) 8
Correct Answer: B
Solution :
\[I=\int_{1}^{5}{\,[|x-3|]}\,dx\]\[\Rightarrow I=\int_{1}^{3}{[-(x-3)]\,dx+\int_{3}^{5}{\,\left[ (x-3) \right]}\,dx}\] \[\Rightarrow I=\int_{1}^{2}{\,[-(x-3)}]dx+\,\int_{2}^{3}{\,[-(x-3)]dx+}\int_{3}^{4}{[x-3]\,dx+\int_{4}^{5}{\,[x-3]\,dx}}\] \[\Rightarrow I=\int_{1}^{2}{\,dx}+\int_{2}^{3}{0\,dx+\int_{3}^{4}{0\,dx+\int_{4}^{5}{\,dx}}}\]\[=[x]_{1}^{2}+[x]_{4}^{5}\] \[\Rightarrow I=(2-1)+(5-4)=2\].
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