Practice Exam

# Practice Exam - MIT OpenCourseWare http:/ocw.mit.edu 18.01...

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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Fall 200 6

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18.01 Practice Exam 4 1 / 2 2 x Problem 1. (15) Evaluate dx by making a trigonometric substitution; remember 0 1 x 2 to change the limits also. Problem 2. (15) Find the volume of the solid obtained by rotating about the y -axis (that’s the y -axis) the area under the graph of y = e x and over the interval 0 ± x ± 1 . (Suggestion: use cylindrical shells.) 4 x Problem 3. (20) Evaluate dx . ( x 2 1)( x 1) (Begin by factoring the denominator completely; don’t forget the ±nal integration.) Problem 4. (15: 8, 7) a) Write down the de±nite integral of the form b a f ( x ) dx which represents the arclength of the curve y = sin 2 x for 0 ± x ± / 4. b) Show that the arclength is less than 1.2 by estimating the integral. (Indicate
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## This note was uploaded on 10/10/2011 for the course MATH 31 taught by Professor Blake during the Spring '11 term at MIT.

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Practice Exam - MIT OpenCourseWare http:/ocw.mit.edu 18.01...

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