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ipn [44]
1 year ago
10

The sum ∫2−2() ∫52()−∫−1−2() can be written as a single integral in the form ∫() determine and

Mathematics
1 answer:
kow [346]1 year ago
6 0

We have

\displaystyle \int_{-2}^2 f(x) \, dx - \int_{-2}^{-1} f(x) \, dx = \int_{-1}^2 f(x) \, dx

so that

\displaystyle \int_{-2}^2 f(x) \, dx + \int_2^5 f(x) \, dx - \int_{-2}^{-1} f(x) \, dx \\\\ ~~~~~~~~~~~~ =  \int_{-1}^2 f(x) \, dx + \int_2^5 f(x) \, dx \\\\ ~~~~~~~~~~~~ = \boxed{\int_{-1}^5 f(x) \, dx}

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