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Question: Answered & Verified by Expert
If \( \int_{0}^{10 \pi+\alpha}|\sin x| d x=k-\cos \alpha \), where \( 0 < \alpha < \pi \), then \( k= \)
MathematicsDefinite IntegrationJEE Main
Options:
  • A \( 101 \)
  • B \( 100 \)
  • C \( 201 \)
  • D none of these
Solution:
2955 Upvotes Verified Answer
The correct answer is: \( 201 \)

Let I=0100π+αsin x dx

=0100πsin x dx+100π100π+αsin x dx

=1000πsin x dx+0αsin x dx   

 Period of sin x is π & 0<α<π

=100 -cosx0π+-cosx0α

=100 1+1+-cos α+1=201-cos α

 k=201

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