Pre-Calc Homework Solutions 314

# Pre-Calc Homework Solutions 314 - 314 7 Section 7.5 8 0 7...

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8. E 7 0 p cos 2 x dx 9. E 7 0 p 1 } 2 y } 2 2 (10 2 y ) dy 10. E 7 0 } ˇ 4 3 w } sin 2 x dx Section 7.5 Exercises 1. E 5 0 xe 2 x /3 dx 5 3 2 3 e 2 x /3 (3 1 x ) 4 5 2 } e 2 5 4 /3 } 1 9 < 4.4670 J 2. E 3 0 x sin 1 } p 4 x } 2 dx 5 } p 4 } 3 } p 4 } sin 1 } p 4 x } 2 2 x cos 1 } p 4 x } 24 5 } 4 ˇ p 2 w } 1 } p 2 } 1 } 3 2 } 2 < 3.8473 J 3. E 3 0 x ˇ 9 w 2 w x w 2 w dx 5 3 2 } 1 3 } (9 2 x 2 ) 3/2 4 5 9 J 4. E 10 0 ( e sin x cos x 1 2) dx 5 3 e sin x 1 2 x 4 5 e sin 10 1 19 < 19.5804 J 5. When the bucket is x m off the ground, the water weighs F ( x ) 5 490 1 } 20 2 2 0 x } 2 5 490 1 1 2 } 2 x 0 } 2 5 490 2 24.5 x N. Then W 5 E 20 0 (490 2 24.5 x ) dx 5 3 490 x 2 12.25 x 2 4 5 4900 J. 6. When the bucket is x m off the ground, the water weighs F ( x ) 5 490 1 } 20 2 20 4 x /5 } 2 5 490 1 1 2 } 2 x 5 } 2 5 490 2 19.6 x N. Then W 5 E 20 0 (490 2 19.6 x ) dx 5 3 490 x 2 9.8 x 2 4 5 5880 J. 7. When the bag is x ft off the ground, the sand weighs F ( x ) 5 144 1 } 18 2 18 x /2 } 2 5 144 1 1 2 } 3 x 6 } 2 5 144 2 4 x lb. Then W 5 E 18 0 (144 2 4 x ) dx 5 3 144 x 2 2 x 2 4 5 1944 ft-lb 8. (a) F 5 ks , so 800 5 k (14 2 10) and k 5 200 lb/in. (b) F ( x ) 5 200 x , and E 2 0 200 x dx 5 3 100 x 2 4 5 400 in.-lb.
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