Area Question 14

Question 14

  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=(gf)(x) and the lines x=α,x=β and y=0, is

(2018 Main) (a) 12(31) (b) 12(3+1) (c) 12(32) (d) 12(21)

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Solution:

  1. We have,
18x29πx+π2 =0
18x26πx3πx+π2 =0
(6xπ)(3xπ) =0
x =π6,π3
Now, α<β α =π6,
β =π3

322 Area

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=π/6π/3cosxdx A=[sinx]π/6π/3 A=sinπ3sinπ6=3212 A=312



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