Exam3Revf06 - MATH 1431 EXAM 3 REVIEW Let f(x) = x2 4x + 6...

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MATH 1431 EXAM 3 REVIEW Upper sums, lower sums, Riemann sums Let f ( x )= x 2 - 4 x +6 on [ - 1 , 4], and let P = {- 1 , 0 , 1 , 2 , 3 , 4 } be a partition of [ - 1 , 4]. -1 1 2 3 4 x 2 4 6 8 10 y 1. Calculate the lower sum L f ( P ) and the upper sum U f ( P ). 2. Let s 1 ,s 2 3 4 be the midpoints o f the subintervals determined by P . Use these values to calculate the corresponding Riemann sum S ( P ). 3. Calculate ± 4 0 f ( x ) dx . Which of the values in (a) and (b) gives the best approximation of the deFnite integral? 4. Calculate the average value of f on the interval [0 , 4]. The Fundamental Theorem of Calculus; Properties of the De±nite Integral 1. Show that F ( x x 16 + x 2 is an antiderivative for f ( x 16 (16 + x 2 ) 3 / 2 . Use this result to evaluate ± 3 0 16 (16 + x 2 ) 3 / 2 dx . 2. The function G is deFned by: G ( x ± cos x 1 t ² 1 - t 2 dt . ( i ) Determine G (2 π )( ii ) Determine G ± ( π/ 6) 3. Evaluate the deFnite integral ± 1 0 5 x (1 + x 2 ) 4 dx . 4. Assume that f is a continuous function and that ± 2 0 f ( x ) dx =3 , ± 3 0 f ( x ) dx =1 , ± 5 3 f ( x ) dx =8 .
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This note was uploaded on 11/27/2008 for the course MATH 1431 taught by Professor Any during the Spring '08 term at University of Houston.

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Exam3Revf06 - MATH 1431 EXAM 3 REVIEW Let f(x) = x2 4x + 6...

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