practicefinal

# practicefinal - 16B Calculus Francisco Santos 8-10am...

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16B Calculus Francisco Santos Dec 11, 2007 8-10am Practice Final (1003 Giedt) Name: ID: 1. ( points) Evaluate the following indeﬁnite integrals. Simplify your answers as much as pos- sible. Show your work. You may use u -substitution, trig formulas, the simple power rule, the fundamental theorem of calculus, integration by parts, partial fraction decomposition, the given integral tables, etc. a. R p 1 + x dx = b. R x 5 ln x dx = c. R x cos x dx = d. R 3 x +5 x 2 - 4 dx = e. R x - 4 x 3 + x 2 dx = f. R 1 x x +1 dx = g. R x ln( x + 1) dx = h. R ln(2 x - 5 ) x dx = i. Bonus (this is a bit hard) R (ln x ) 2 dx = 2. ( points) Evaluate the following deﬁnite integrals. (Note, some may even be improper.) Simplify your answers as much as possible. Show your work. You may use u -substitution, trig formulas, the simple power rule, the fundamental theorem of calculus, integration by parts, partial fraction decomposition, the given integral tables, etc. a. R 4 2 1 3 x - 3 dx = b. R e 2 1 1 1+ x 1 / 2 dx = c. R 1 1 1+ x 1 / 2 dx =

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Name: ID: 2 d. R 1 0 1 x 2 dx = e. R -∞ 1 x 2 dx = f. R 0 x 2 e - x 3 dx = g. R 0 -∞ x 2 e - x 3 dx = h. R 2 0 4 x 2 + 16 x dx = [Hint: see tables] i. R 2 0 xe x dx = Circle the correct answer from the list below: (a) 2 e 2 - 1 (b) 1 - e 2 (c) 1 + e 2 (d) (diverges) (e) none of the above 3. ( points) a. Find the area of the region bounded by the graphs of f ( x ) = 3
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practicefinal - 16B Calculus Francisco Santos 8-10am...

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