w01-1 - Math 152 Workshop 1 Spring 2011 1. Suppose that f...

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Math 152 Workshop 1 Spring 2011 1. Suppose that f is a continuous function (defined for all x ) and that it is known that Z 1 0 f ( x ) dx = 5 , Z 1 - 1 f ( x ) dx = 3 , Z 2 0 f ( x ) dx = 8 and Z 4 0 f ( x ) dx = 11 . Evaluate the integrals: (a) Z 2 0 f (2 x ) dx (b) Z π 0 (sin x ) f (cos x ) dx (c) Z 3 2 xf (8 - x 2 ) dx . ( Suggestion: Use substitutions, such as u = cos x in (b).) 2. Sketch the region R defined by 0 y 1 /x 3 , 1 x 2. (a) Find (exactly) the number a such that the line x = a divides R into two parts of equal area. (b) Then find (to 3 places) the number b such that the line y = b divides R into two parts of equal area. 3. Which has more area, the region in the first quadrant enclosed by the line x + y = 1 and the circle x 2 +
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