10FallHwk11

10FallHwk11 - Math 2413 Homework Set 11 10 Points...

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Math 2413 Homework Set 11 10 Points Substitution Rule for Definite Integrals Compute each of the following integrals. Clearly show the substitution used for each integral and how it was used. In other words, don’t just write an answer down for any of these. 1. ( ) 1 6 23 0 2 t t dt - - & 2. () 2 1 sin 0 cos x x dx p + & e 3. 3 3 1 1 42 z dz z + + ± ² ı 4. ( ) () () 2 2 co s si n cos y y y dy + & 5. 7 2 3 11 43 12 dx xx - +- ± ² ı Area Between Curves For problems 6 – 8 graph the enclosed region and find the area of the region. Note that you can use computational aids to do the graphs, but I do expect to see a sketch in your homework! 6. The area bounded by 1 2 2 x y - =- e , x y - =+ e , 1 x and 2 x = . Note that these curves don’t intersect inside this interval so you don’t need to worry about that for this problem. 7. The area bounded by ( ) 2 2 yx , 2 4 , 1 x and 4 x = . 8. The area bounded by 2 6 xyy = -- and 2 4 xy . Volumes – Method of Rings For problems 9 – 11 graph the bounding region as well as an attempt at graphing the solid of revolution and a representative ring/disk.
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10FallHwk11 - Math 2413 Homework Set 11 10 Points...

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