Question

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

Answer 1

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}`