GATE | Gate IT 2005 | Question 35

What is the value of 

(A) -1
(B) 1
(C) 0
(D) π

Answer: (B)
Explanation:

In the above  integral 

f(x) = (x- π)^3 (sinx)

f(2π – x) = (2π – x – π)^3 (sinx)

              = (π – x )^3 (sinx)

              =  -( x – π  )^3 (sinx)

               =-f(x)

so ,  ∫ (x- π)^3 (sinx) dx =1

since , 

  ∫f(x)dx= 1

whenever f(2π – x)  = -f(x)

hence option B is correct

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