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0+w|sinx|dx, where nN and 0w<π is equal to

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a
(2n + 1) + sin w
b
2n + cos w
c
(2n + 1) - cos w
d
None of these

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detailed solution

Correct option is C

I=∫0nπ+w |sin⁡x|dx  =∫0w |sin⁡x|dx+∫wnπ+w |sin⁡x|dx=I1+I2I1=∫0w |sin⁡x|dx=∫0w sin⁡xdx =−[cos⁡x]0w=−cos⁡w+1=1−cos⁡wI2=∫wnπ+w |sin⁡x|dx=n∫0π |(sin⁡x)|dx =n∫0π sin⁡xdx=n[−cos⁡x]0π=2nso, I=1−cos⁡w+2n=(2n+1)−cos⁡w


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