Let α and β α < β are roots of 18 x 2 - 9 π x + π 2 = 0 ,   f x = x 2 ,   g x = cos x . Then ∫ α β x g o f x d x =

Question

Let &#945; and &#946; &#945; &#60; &#946; are roots of 18 x 2 - 9 &#960; x + &#960; 2 = 0 , &#160; f x = x 2 , &#160; g x = cos x . Then &#8747; &#945; &#946; x g o f x d x =

Aicharya · Accepted Answer

Given f x = x 2 , &#160; g x = cos x i.e. g f x = cos x 2 For 18 x 2 - 9 &#960; x + &#960; 2 = 0 roots are 9 &#960; &#177; 81 &#960; 2 - 72 &#960; 2 36 = 9 &#960; &#177; 3 &#960; 36 = &#960; 3 , &#160; &#960; 6 i.e. &#945; = &#960; 6 , &#160; &#946; = &#960; 3 So, &#8747; &#945; &#946; x g &#8728; f x d x = &#8747; &#960; 6 &#960; 3 x cos x 2 d x Let x 2 = t ; &#160; x d x = d t 2 1 2 &#8747; &#960; 2 36 &#960; 2 9 cos t d t = 1 2 sin &#960; 2 9 - sin &#960; 2 36

Let α and β α < β are roots of 18 x 2 - 9 π x + π 2 = 0 ,   f x = x 2…

Solution

Let &#945; and &#946; &#945; &#60; &#946; are roots of 18 x 2 - 9 &#960; x + &#960; 2 = 0 , &#160; f x = x 2…

Solution

Let α and β α < β are roots of 18 x 2 - 9 π x + π 2 = 0 , f x = x 2…