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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(3)+1)`

B

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

C

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

D

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

Text Solution

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The correct Answer is:
D
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