Let q∈N and p∈(−π2,π2). Then, the value of p+qπ∫0|cosx|dx is
A
2q+sinp
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B
2q+1−sinp
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C
2q+cosp
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D
2q−1+cosp
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Solution
The correct option is A2q+sinp Let I=p+qπ∫0|cosx|dx ⇒I=p∫0|cosx|dx+p+qπ∫p|cosx|dx
Using the property: a+nT∫af(x)dx=nT∫0f(x)dx[Tis the period off(x)]⇒I=p∫0|cosx|dx+qπ∫0|cosx|dx⇒I=[sinx]p0+2qπ2∫0(cosx)dx⇒I=2q+sinp