Calculus 2-A1 - Calculus II Calculus: Early Transcendental...

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Calculus II Calculus: Early Transcendental Functions , 4th ed., by Ron Larson, Robert Hostetler, and Bruce H. Edwards (Boston: Houghton Mifflin, 2007; ISBN-10: 0-618-60624-6). Written Assignment 1 Complete the following textbook exercises for sections 7.2, 7.3, and 7.4, and submit them to your mentor for correction and grading. Show all calculations. SECTION 7.2 Exercises Do exercises 2, 4, 8, 10, 12, 14, 20, and 26 on pages 463–464 of the textbook. #2 set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x- axis. V=πƒ 0 2 [R(x)] 2 dx V=πƒ 0 2 [ 4-x 2 ] 2 dx V=πƒ 0 2 [16 + x 4 - 8x 2 ]dx V=π [16x + (x 5 /5) – (8/3)x 3 ] 0 2 V=π [32+(32/5) – (64/3)] V=π [(480+96-320/15)] V= (256/15)π
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V=πƒ 0 3 [R(x)] 2 dx V=πƒ 0 3 [√(9-x 2 )] 2 dx V=πƒ 0 3 (9-x 2 ) dx V=πƒ 0 3 (9-x 2 ) dx V=π [9-x 3 /3] 0 3 V=π [9 * 3 -9] V=18π #8. set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y- axis. V=πƒ 0 4 [R(y)] 2 dy V=πƒ 0 4 [√(16-y 2 )] 2 dy V=π [16-y 2 ] 0 4 V=π [16y-y 3 /3] 0 4 V=π [64-64/3] V=128π/3
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V=πƒ 1 4 [R(y)] 2 dy V=πƒ 1 4 [-y 2 + 4y] 2 dy V=πƒ 1 4 [16y 2 + y 4 - 8y 3 ] dy V=π [(16/3) y 3 +y 5 /5 – (8/4)y 4 ] V=π [(16/3 64 + 1024/5 – 8*64) – (16/3+1/5-2)] V=π [(5120+3-72-7680)/15 – (80 + 3 -30)/15] V=π[512/15 – 53/15] V=(459/15)π V=153π/5 #12 find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. (a) y= 2x 2 => x=√y/2, r(y) =√y/2, R(y) = 2 therefore when x=2, y=8 V=πƒ 0 8 [R(y)] 2 dy V=πƒ 0 8 [2 2 ( √y/2 )] 2 dy V=πƒ 0 8 [4 - y/2 ]dy V=π [4y – y 2 /4 ] 0 8 V=π [32 – 16] V= 16π (b) volume of the resulting solid V=πƒ 0 2 [R(x)] 2 dx V=πƒ 0 2 [2x 2 ] 2 dx V=πƒ 0 2 [4x 4 ]dx V= 4π[x 5 /5] 0 2 V= 4π [32/5]
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Calculus 2-A1 - Calculus II Calculus: Early Transcendental...

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