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Unformatted text preview: Section 5.3
4 5 217 (b) Area
0 (x 2 4x) dx
4 (x 2 4x) dx F(4)]
32 3 1 3 x 3 30. The region between the graph and the xaxis is a rectangle with a half circle of radius 1 cut out. The area of the region 13 is 2(1) av( f )
1 2 1 (1)2 2
1 [F(4)
32 3 F(0)] 0 [F(5)
25 3 4 2 .
4 4 f (t) dt
1 25. An antiderivative of x 2 av
1 3 1 3 1 3
0 3 1 is F(x) x. 1 4 2 2 . (x 2 F( (0 3) 0) 1) dx F(0) 0 1 0 31. There are equal areas above and below the xaxis. av( f )
1 2
2 f (t) dt
0 1 2 0 0 32. Since tan is an odd function, there are equal areas above Find x c in [0, 3] such that c2 c2 1 c 1 Since 1 is in [0, 3], x 1.
2 and below the xaxis. av( f )
1 /2
/4 f( ) d
/4 2 0 0 33. min f
x x 26. An antiderivative of is F(x) . 2 6 3 1 x2 1 1 av dx [F(3) F(0)] 3 0 2 3 3 c2 3 Find x c in [0, 3] such that . 2 2
3 9 2 3 2 1 2 1 and max f 2 1 1 dx 1 x4 0 1 16 17
0.5 0 1 34. f (0.5)
1 2 8 17 1 2 1 4 8 17 49 68 16 17 c2 c 1 1 x4 3 3 3 is in [0, 3], x 3x 2 3. 1 is F(x) F(1) F(0) 3c2 1 x
3 dx
1 2 1 (1) 2 0.5 0 1 1 Since 27. An antiderivative of av
1 1
1 0 x. ( 3x 2 1) dx 2 2 Find x 3c2 c c Since
2 c in [0, 1] such that 1 x4 1 1 1 2 x4 0.5 1 1 1 dx x4 0.5 1 1 1 1 4 x4 0 1 1 1 dx x4 0 1 dx dx
8 17 1 16 2 17 dx
33 34 1 2 8 17 35. max sin (x 2 )
1 0 sin (1) on [0, 1] sin (1) 1 x 8 2 2 on [0, 1] 1 3 1 3 1 3 sin (x 2 ) dx x
1 0 36. max is in [0, 1]. x
1 3 8 x 3 and min 8 dx 3 .
1 (x 1)3. 3 1 8 1 F(0)] 3 3 3
2 2 2 37. (b 1 0 38. (b
b a 28. An antiderivative of (x av
1 3
3 1)2 is F(x)
1 [F(3) 3 a) min f (x) (b 0 on [a, b]
b (x
0 1)2 dx a) min f (x)
a f (x) dx Find x c in [0, 3] such that (c 1) 1. c 1 1 c 2 or c 0. Since both are in [0, 3], x 0 or x 2. 29. The region between the graph and the xaxis is a triangle of height 3 and base 6, so the area of the region is (3)(6) av( f )
1 6
2 a) max f (x) f (x) dx (b 0 on [a, b] a) max f (x) 0 1 2 9. f (x) dx
4 9 6 3 2 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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