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\( 3.5 \)
\( \int_{0.2}[x] d x \) is equal to
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\( \int_{0.2}[x] d x \) is equal to
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The correct answer is:
\( 4.5 \)
Given that,
$\int_{0.2}^{3.5}[x] d x$
$=\int_{0.2}^{1} 0 \cdot d x+\int_{1}^{2} 1 . d x+\int_{2}^{3} 2 . d x+\int_{3}^{3.5} 3 d x$
$=0+1[x]_{1}^{2}+2[x]_{2}^{3}+3[x]_{3}^{3.5}$
$=0+1(2-1)+2(3-2)+3(3.5-3)$
$=0+1+2+1.5=4.5$
$\int_{0.2}^{3.5}[x] d x$
$=\int_{0.2}^{1} 0 \cdot d x+\int_{1}^{2} 1 . d x+\int_{2}^{3} 2 . d x+\int_{3}^{3.5} 3 d x$
$=0+1[x]_{1}^{2}+2[x]_{2}^{3}+3[x]_{3}^{3.5}$
$=0+1(2-1)+2(3-2)+3(3.5-3)$
$=0+1+2+1.5=4.5$
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