Let g_ i : [ 8 , 3 8 ] R , i=1,2 , and f: [ 8 , 3 8 ] R be functions such that g₁(x)=1, g₂(x)=|4 x- | and f(x)= ² x , for all x [ 8 , 3 8 ] Define S_ i = _ 8 ^ 3 8 f(x) g_ i (x) d x, i=1,2 The value of 16 S 1 π is ___.

Question

Let g_ i : [ 8 , 3 8 ] R , i=1,2 , and f: [ 8 , 3 8 ] R be functions such that g₁(x)=1, g₂(x)=|4 x- | and f(x)= ² x , for all x [ 8 , 3 8 ] Define S_ i = _ 8 ^ 3 8 f(x) g_ i (x) d x, i=1,2 The value of 16 S 1 &#960; is ___.

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S 1 = &#8747; &#960; 8 3 &#960; 8 sin 2 x &#183; 1 d x &#160; &#160; &#160; &#160; &#8230; &#8230; . . . i S 1 = &#8747; &#960; 8 3 &#960; 8 sin 2 3 &#960; 8 + &#960; 8 - x d x S 1 = &#8747; &#960; 8 3 &#960; 8 cos 2 x d x &#160; &#160; &#160; &#8230; &#8230; . . ii From (i) and (ii), we get 2 S 1 = &#8747; &#960; 8 3 &#960; 8 1 d x 2 S 1 = &#960; 4 16 &#160; S 1 &#960; = 2

Let g_ i : [ 8 , 3 8 ] R , i=1,2 , and f: [ 8 , 3 8 ] R be functions such that g₁(x)=1, g₂(x)=|4 x- | and f(x)= ² x , for all x [ 8 , 3 8 ] Define S_ i = _ 8 ^ 3 8 f(x) g_ i (x) d x, i=1,2 The value of 16 S 1 π is ___.

Correct answer

Step-by-step solution

More from Definite Integration

Let g_ i : [ 8 , 3 8 ] R , i=1,2 , and f: [ 8 , 3 8 ] R be functions such that g₁(x)=1, g₂(x)=|4 x- | and f(x)= ² x , for all x [ 8 , 3 8 ] Define S_ i = _ 8 ^ 3 8 f(x) g_ i (x) d x, i=1,2 The value of 16 S 1 &#960; is ___.

Correct answer

Step-by-step solution

More from Definite Integration

Let g_ i : [ 8 , 3 8 ] R , i=1,2 , and f: [ 8 , 3 8 ] R be functions such that g₁(x)=1, g₂(x)=|4 x- | and f(x)= ² x , for all x [ 8 , 3 8 ] Define S_ i = _ 8 ^ 3 8 f(x) g_ i (x) d x, i=1,2 The value of 16 S 1 π is ___.