Example 43 - Evaluate integral |x sin (pi x)| dx - Examples

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Example 43 (Introduction) Evaluate 1 3 2 sin We have sin , where 1< < 3 2 (i) < 0 1 < 0 > 0 0 < 3 2 (ii) 1 3 2 3 2 Let = 3 2 From graph it is seen, sin <0 <0 sin >0 0 < sin <0 3 2 That is, Hence, we have Example 43 Evaluate 1 3 2 sin Hence, ( ) = sin 1 1 & sin 1 3 2 1 3 2 sin = 1 1 sin 1 3 2 sin ( ) Solving separately sin sin = ( )( sin ) = x sin sin = x ( cos ) 1 cos = cos + cos = cos + sin 2 Putting limits Hence answer = 2 1 2 + 1 = 2 + 1 2 + 1 = +

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