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integration between (-1to 3/2) of |x sin((pi)x)|=kp 2 .find the value of k? (where | | is the modulus function)

integration between  (-1to 3/2) of |x sin((pi)x)|=kp2.find the value of k? (where | | is the modulus function)

Grade:12

1 Answers

Ramesh V
70 Points
11 years ago

For x:   -1<x<0        |x sin((pi)x)| is positive

For x:   0<x<1          |x sin((pi)x)| is positive

For x:   1<x<3/2       |x sin((pi)x)| is negative

so, its

integration from (-1 to 1)  x sin((pi)x).dx  -   integration from (1 to 3/2)  x sin((pi)x).dx

integral of x sin((pi)x).dx  is       -x.cos((pi)x)/Pi  +  sin((pi)x)/(Pi)2

so value is

1/Pi -  1/(Pi)2

 


 

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