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Question
Evaluate the following:
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}` Find 'c" if `int_0^1 "f"(x) "d"x` = 2
Sum
Solution
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}`
⇒ `int_0^1 "f"(x) "d"x` = 2
⇒ `int_0^2 "c"x "d"x` = 2
`"c"[x^2/2]_0^1` = 2
`"c"[1/2 - 0]` = 2
`1/2` = 2
⇒ c = 4
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Definite Integrals
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