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1)

Let g(x)=cosx2,f(x)=x and α,β(α<β) be the roots of the quadratic equation  

18x29πx+π2=0 .Then , the area (in sq units) bounded by the curve  y=(gof)(x) and the lines x=α, x=β

 and y=0, is 


A) 12(31)

B) 12(3+1)

C) 12(32)

D) 12(21)

Answer:

Option A

Explanation:

We have 

    18x29πx+π2=0

   18x26πx3πx+π2=0

 (6xπ)(3xπ)=0

       x=π6,π3

 Now ,  α<β=π6,β=π3

  Given  g(x)=cosx2 and  f(x)=x

       y=gOf(x)

           y=g(f(x))=cosx

    Area of region bounded by x=α,

  x=β , y=0 and curve  y=g(f(x)) is

    A=π3π6cosxdx

    A=[sinx]π3π6

    A=sinπ3sinπ6=3212

      A=(312)