10Bquiz1sol

10Bquiz1sol - g ( x )) 2 dx . Find the integral value Z b a...

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Quiz 1 Solution for MATH 10 B, 2010 1 . Let f ( x ) = 2 - x . (a) Sketch the graph of f ( x ) . Ans. (b) Find the average value of f ( x ) over the interval [ 0, 2 ] . (Use the geometric interpretation to compute the definite integral. DO NOT use the fundamental theorem of calculus). Ans. Average = 1 2 - 0 Z 2 0 f ( x ) dx = 1 2 ( area under the curve f ( x ) = 2 - x for 0 x 2) = 1 2 ± 1 2 · 2 · 2 ² = 1 2 . Let Z b a f ( x ) dx = 8, Z b a ( f ( x )) 2 dx = 12, Z b a g ( x ) dx = 2, Z b a (
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Unformatted text preview: g ( x )) 2 dx . Find the integral value Z b a [ c 1 g ( x ) + ( c 2 f ( x )) 2 ] dx where c 1 , c 2 are constants. Ans. Z b a [ c 1 g ( x ) + ( c 2 f ( x )) 2 ] dx = c 1 Z b a g ( x ) dx + ( c 2 ) 2 Z b a f 2 ( x ) dx = c 1 2 + ( c 2 ) 2 12 = 2 c 1 + 12 ( c 2 ) 2...
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