Question

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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\tt I = \int\limits _{-2}^{2} |x| \:dx \\ \\ \tt We\:know\:the\:property \\ \\ \tt \int\limits_{-a}^{a} f(x) \:dx = 0 \: \: \: \: For \: odd \: function \\ \tt = 2\int\limits_{0}^{a} f(x) \: dx \: \: \: \: For\:evev\:functions\\ \\ \tt Let's \:check\:our\:function\:is\:even\:or\:odd \\ \\ \tt f(x) = |x| \\ \\ \tt \longrightarrow f(-x) = | -x | \\ \\ \tt \longrightarrow f(-x) = |x| \\ \\ \tt \longrightarrow f(x) = f(-x) \\ \\ \tt So\: the\:function\:is\:even\\ \\ \tt \longrightarrow I = \int\limits_{0}^{2} |x| \: dx \\ \\ \tt \longrightarrow I = \int\limits_{0}^{2} x \:dx \\ \\ \tt \longrightarrow I = {(\frac{{x}^{2}}{2})}^{2}_{0}\\ \\ \tt \longrightarrow I = \frac{{2}^{2}}{2} \\ \\ \tt \longrightarrow I = 2 \\ \\ \boxed{\bold{\underline{\red{\tt \int\limits_{-2}^{2} |x|\:dx = 2 }}}}$