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Let g(x) = cosx^(2), f(x) = sqrt(x), a...

Let `g(x) = cosx^(2), f(x) = sqrt(x)`, and `alpha, beta (alpha lt beta)` be the roots of the quadratic equation `18x^(2) -9pix + pi^(2) = 0`. Then the area (in sq. units) bounded by the curve `y = (gof) (x)` and the lines `x = alpha,x = beta` and `y = 0` is

A

`1/2(sqrt(2)-1)`

B

`1/2(sqrt(3)-1)`

C

`1/2(sqrt(3) +1)`

D

`1/2(sqrt(3)-sqrt(2))`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let g (x) =x ^(2),f (x) = sqrtx, and alpha, beta ( alpha lt beta) be the roots of the quadratic equation 18 x ^(2) - 9pix + pi^(2) =0. Then the area (is sq. units) bounded by curve y = (gof) (x) and the lines x =alpha, x = betaand y =0 is :

    A
    `(pi^2)/24`
    B
    `(pi^2)/9`
    C
    `(pi^2)/36`
    D
    `(pi^2)/72`

  • Let f(x)=x^(2), g(x)="cos" x and alpha,beta (alpha lt beta) be the roots of the equation 18x^(2)-19pi x+pi^(2)=0 . Then the area bounded by the curves u="fog"(x) , the ordinates x=alpha, x=beta and the X-asis is

    A
    `(1)/(2)(pi-3)` sq units
    B
    `(pi)/(3)` sq units
    C
    `(pi)/(4)` sq units
    D
    None of these

  • Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

    A
    `alpha^(2) +beta^(2) =4`
    B
    `(alpha - beta)^(2)=3`
    C
    `alpha^(3) +beta^(3)=2`
    D
    `alpha^(4) +beta^(4) = 1`

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