Evaluate the following integral: `int_(-pi//2)^(pi//2)(2sin|x|+cos x)dx`

Explanation

Let,I=`int_(-pi//2)^(pi//2)(2sin|x|+cos x)dx`

Here `f(x)=2sin|x|+cos x`

f(x)=-f(x)

Thus,I=`int_(-pi//2)^(pi//2)(2sin|x|+cos x)dx`

I=`2int_(0)^(pi//2)(2sinx+cos x)dx`

I=`2int_(0)^(pi//2)(-2cosx+sin x)dx`

I=`2(-2cos(pi/2)+sin (pi/2)+2cos0-sin0)dx`

I=`2(1+2)`

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