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Unformatted text preview: Section 5.3
7. An antiderivative of 7 is F(x)
1 215 7x. 21
5 2 x 2 17. Divide the shaded area as follows. 14
3 R2 R1 y = x2 1 2 x y 7 dx
3 F(1) F(3) 7 8. An antiderivative of 5x is F(x)
2 5x dx
0 F(2) F(0) 10 0 10 9. An antiderivative of
5 3 x dx 8 F(5) x is F(x) 8 25 F(3) 16 x2 . 16 9 1 16 R3 10. An antiderivative of 2t
2 3 is F(t) F(0) 2 t2 0
1 2 t 2 3t. 2 t 2. 0
z2 . 4 7 4
1 Note that an antiderivative of x 2 Area of R1 Area of R2 1 3
1 1 is F(x) 1 3 x 3 x. (2t
0 3) dt F(2) 3(1) (3)(1) 3
2 (x 2 1) dx 11. An antiderivative of t
2 2 is F(t) F(0) z 3 1 3 [F(2)
2 3 F(1)]
2 3 5 3 (t
0 2) dt F( 2) 1 12. An antiderivative of 1
1 1
2 z dz 2 F(1)
1 1 z is F(z) 2 5 F(2) 4 x2 Area of R3 (x 2 1) dx F(0)] 0
2 3 2 3 16 3 0 [F(1)
2 3 13. An antiderivative of
1 11 is F(x)
4 tan x.
2
1 1 x2 dx F(1) F( 1)
1 1 x2 4 Total shaded area 3 5 3 14. An antiderivative of
1/2 1/2 is F(x)
1 2 6 sin x.
3 18. Divide the shaded area as follows.
y 3 R1 y = 3 3x 2 2 R2 R3 9 x dx 1 x2 1 F 2 F 6 15. An antiderivative of e x is F(x)
2 0 e x. 1 6.389 3 ln x 1. e x dx F(2) F(0)
3 x 1 e2 16. An antiderivative of
3 0 is F(x) 3 dx x 1 F(3) 3 ln 4 3 ln 4 F(0) 0 Note that an antiderivative of 3 4.159 Area of R1 Area of R2 Area of R3
1 3x 2 is F(x) F(1) F(0) 3x 2 x 3. (3
0 3x 2) dx 9
2 (9)(1) (9)(1) (3
1 3x 2) dx 9 9 Total shaded area [F(2) ( 2 2 9 F(1)] 2) 5 5 16 ...
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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
 Derivative

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