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Pre-Calc Homework Solutions 215

# Pre-Calc Homework Solutions 215 - Section 5.3 7 An...

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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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