A) \[0\]
B) \[1/2\]
C) \[1\]
D) \[2\]
Correct Answer: C
Solution :
Let\[I=\int_{0}^{2}{|x-1|}\,\,dx\] \[=\int_{0}^{1}{-(x-1)}\,dx+\int_{1}^{2}{(x-1)}\,dx\] \[=\left[ -\frac{{{x}^{2}}}{2}+x \right]_{0}^{1}+\left[ \frac{{{x}^{2}}}{2}-x \right]_{1}^{2}\] \[=\left[ -\frac{1}{2}+1 \right]+\left[ 2-2-\left( \frac{1}{2}-1 \right) \right]\] \[=\frac{1}{2}+\frac{1}{2}\] \[=1\] Alternative Solution: Let \[I=\int_{0}^{2}{|x-1}|\,\,dx\] It is clear from the figure, Required area = Area of\[\Delta OAD+\]Area of \[\Delta ABC\] \[=\frac{1}{2}\times 1\times 1+\frac{1}{2}\times 1\times 1\] \[=\frac{1}{2}+\frac{1}{2}=1\]You need to login to perform this action.
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