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Mathematics
Problem
In one or two sentences, explain why
∫
a
b
(
f
(
x
)
+
g
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x
)
)
d
x
\displaystyle\int_a^b\bigl(f(x)+g(x)\bigr)\,dx
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f
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equals
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f
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d
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+
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a
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g
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d
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\displaystyle\int_a^b f(x)\,dx+\int_a^b g(x)\,dx
∫
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f
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d
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+
∫
a
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g
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d
x
by referring to the interpretation of a definite integral as net signed area.
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