Q. 135.0( 1 Vote )

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Answer :

Let us assume



.....….equation 1


By property we know that


Thus



.....equation 2


Adding equation 1 and equation 2



We know



……equation


Let cosx = y


Differentiating both sides


– sinxdx = dy


sinxdx = – dy


for x = 0


cos0 = y


1 = y


For x = π


cosπ = y


– 1 = y


Substituting equation 3 becomes






2I = π[{3(1) – (1)3} – {3( – 1) – ( – 1)3}]/3


2I = π[2 – { – 3 + 1}]/3


2I = π[2 + 2]/3


I = 2π/3


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