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Question
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
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Solution
We have, `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
Let f(x) = sin|x| + cos|x|
Then, f(x) = f(–x)
Since, f(x) is an even function
So, I = `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
= `2int_0^(π/2) (sinx + cosx)dx`
= `2[-cosx + sinx]_0^(π/2)`
= `2[-cos π/2 + sin π/2 + cos0 - sin0]`
= 2[0 + 1 + 1 – 0]
= 2(2)
= 4
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