Quiz 2 Key - QUIZ 2 Solution Keys Math 141/6380 Due...

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QUIZ # 2 Solution Keys Math 141/6380, Due 11:59PM, Sunday, June 11, 2017 1. The area enclosed between ? = ?2+ 2and ? = 3is revolved about the horizontal line ? = 3to form a solid. Calculate the volume. (Hint: Disks) Solution: Let ??+ ? = ?, 𝐭𝐡𝐞𝐧 ? = −? & ? = ?. The radius function 𝒓(?) = ??− ?for −? ≤ ? ≤ ?. 𝑨(?) = 𝝅{𝒓(?)}?= 𝝅(??− ?)?= 𝝅(??− ???+ ?).15161325113251)1(1)1(32)1(51)1(1)1(32)1(5113251)12()}({353511351124112xxxdxxxdxxrV2. Let Rbe the region between the graphs of f(x) and g(x)on the given interval. Find the volume Vof the solid obtained by revolving Rabout the x-axis, where 3)(xxfand 13)(2xxgx[0, 4]. Hint: Solids with HolesSolution: ? (?)is above ?(?) over the interval [?, ?]31373112)32483128()0(8)0(3)0(32)4(8)4(3)4(328332)862()]13()96[()133})]([)]({[232340234040222402224022xxxdxxxdxxxxdxxxdxxgxfV

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