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Let g(x)=cos^2 x,f(x)=sqrtx and alpha,...

Let `g(x)=cos^2 x,f(x)=sqrtx and alpha,beta (alpha

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:
To find the area bounded by the curve \( y = (g \circ f)(x) \) and the lines \( x = \alpha \), \( x = \beta \), and \( y = 0 \), we will follow these steps: ### Step 1: Identify the functions and roots We have: - \( g(x) = \cos^2 x \) - \( f(x) = \sqrt{x} \) The roots \( \alpha \) and \( \beta \) are given by the quadratic equation: \[ 18x^2 - 9\pi x + \pi^2 = 0 \]
To find the area bounded by the curve \( y = (g \circ f)(x) \) and the lines \( x = \alpha \), \( x = \beta \), and \( y = 0 \), we will follow these steps: ### Step 1: Identify the functions and roots We have: - \( g(x) = \cos^2 x \) - \( f(x) = \sqrt{x} \) The roots \( \alpha \) and \( \beta \) are given by the quadratic equation: ...
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