172 SPRING 2006 EXAM 1 - by y = x 4 and y = 1 about the...

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Math 172-(4,5,6) EXAM 1 February 15, 2006 Name: ID#: Section#: SHOW APPROPRIATE WORK or EXPLANATION on each problem for full credit. Box or circle your Fnal answers. Calculators/note sheets are NOT allowed. Numbers in the [ ] indicate what each problem is worth. Check the board for useful info. Potentially useful formulas: sin(2 x ) = 2 sin( x ) cos( x ) sin 2 ( x ) = 1 2 [1 - cos(2 x )] cos 2 ( x ) = 1 2 [1 + cos(2 x )] sin 2 ( x ) + cos 2 ( x ) = 1 tan 2 ( x ) + 1 = sec 2 ( x ) sec 2 ( x ) - 1 = tan 2 ( x ) | E M | ≤ K ( b - a ) 3 24 n 2 , where | f ′′ ( x ) | ≤ K on a x b 1. [10] Sketch the region bounded by the curves y = x 4 and y = 1. Then use an integral to Fnd its area. 2. [10] Use the disk/washer method to Fnd the volume of the solid obtained by rotating the region bounded
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Unformatted text preview: by y = x 4 and y = 1 about the x-axis. 3. [10] Using the method of cylindrical shells, SET UP a deFnite integral that would give the volume of the solid obtained by rotating the region bounded by y = x 4 and y = 1 about the line x = 2. 4. [10 each] Evaluate each of the following integrals: a) i x 3 ln( x ) dx b) i e 3 x cos( x ) dx c) i sin 2 ( x ) cos 3 ( x ) dx d) i 1 x 2 ( x-5) dx e) i 9-x 2 dx f) i 1 2 + x dx 5. [10] How large should n be to guarantee that the Midpoint approximation M n for the integral i 3 1 ( x-1 2 x 3 ) dx is accurate to within 0.01?...
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172 SPRING 2006 EXAM 1 - by y = x 4 and y = 1 about the...

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