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B
3π2
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C
7π4
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D
5π6
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Solution
The correct option is C7π4 LetI=∫π204sinx+3cosxsinx+cosxdx=∫π204sin(π2−x)+3cos(π2−x)sin(π2−x)+cos(π2−x)dx =∫π204cosx+3sinxsinx+cosxdx ∴2I=∫π207sinx+7cosxsinx+cosxdx=7∫π20sinx+cosxsinx+cosxdx=7[x]π20=7π2 ∴I=7π4