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$P(1 \leq x \leq 2) = \Large \int_{1}^{2} c x = c \int_{1}^{2}x$

$\large = \frac{1}{8} \int_{1}^{2}x$

$\large = \frac{1}{8} \left [ \frac{x^2}{2} \right ]_1^{2}$

$= \Large\frac{3}{16}$

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