Let g(x) = cosx2, f(x) = $\sqrt x $ and $\alpha ,\beta \left( {\alpha < \beta } \right)$ be the roots of the quadratic equation 18x2 - 9$\pi $x + ${\pi ^2}$ = 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 :

Question

Let g(x) = cosx², f(x) = $\sqrt x $ and $\alpha ,\beta \left( {\alpha < \beta } \right)$ be the roots of the quadratic equation 18x² - 9$\pi $x + ${\pi ^2}$ = 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 :

${1 \over 2}\left( {\sqrt 2 - 1} \right)$

${1 \over 2}\left( {\sqrt 3 - 1} \right)$

${1 \over 2}\left( {\sqrt 3 + 1} \right)$

${1 \over 2}\left( {\sqrt 3 - \sqrt 2 } \right)$

Solution

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