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review2 - Practice Problems for Midterm II MATH 10B 2010...

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Practice Problems for Midterm II, MATH 10 B, 2010 Spring 1 . Evaluate the following integrals. When doing so, state what method you are using (for example, substitution, integration by parts, partial fractions) and show all your work. (a) R ( ln z ) 2 z dz (b) R x sin ( x 2 ) dx (c) R 1 0 x 1 - x 2 dx (d) R pe 0.1 p dp (e) R cos ( x ) sin 2 ( x ) dx (f) R 1 ( x - 2 )( x - 5 ) dx (g) R 1 v 2 + 1 dv (h) R u 1 + u 2 du (i) R 10 1 xe x dx (j) R x 2 x 2 - 1 dx (k) R cos y y dy (l) R sin ( ln x ) 1 x dx (m) R sin ( 2 x ) e 3 x dx (n) R 1 + u 2 du (o) R 1 0 p 1 - y 2 dy 2 . (a) Use the midpoint rule with 5 subdivisions to approximate R 2 1 e - x 2 /2 dx . (Just set up the Rie- mann sum. Do not evaluate). (b) Use the trapezoidal rule with 5 subdivisions to approximate R 2 1 e - x 2 /2 dx . (Just set up the Riemann sum. Do not evaluate). 3 . Evaluate the following improper integrals, if convergent, otherwise explain why it is divergent. (a) Z 1 e - x dx (b) Z 1 e - x 2 dx (c) Z 1 1 x dx (d) Z 1 0 1 x dx 4 . Determine whether the area of the region S = ( x , y ) | 3 x 4, 0 y 1 4 - x is finite, and find the area if it is finite.
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