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Question
If f(x) = `{{:(x^2"e"^(-2x)",", x ≥ 0),(0",", "otherwise"):}`, then evaluate `int_0^oo "f"(x) "d"x`
Sum
Solution
`int_0^oo x^2 "e"^(-2x) "d"x = int_0^oo x^"n""e"^(-"a"x) "d"x`
= `("n"!)/("a"^("n" + 1))`
Where n = 2
a = 2
So `int_0^oo "f"(x) "d"x = (2!)/2^3`
= `2/8`
= `1/4`
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Definite Integrals
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