# Math 141 Quiz 2 Key.pdf - QUIZ 2 Solution Keys Math 141...

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QUIZ # 2 Solution Keys Math 141 6380, Due 11:59PM, Sunday, February 3, 2019 1. The area enclosed between ? = ?2+ 1and ? = 2is revolved about the horizontal line ? = 2to 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()}({353511351124112=++=++=+=+==xxxdxxxdxxrV2. 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)(2+=xxgx[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})]([)]({[232340234040222402224022==++=++++=++=++=+++=++==xxxdxxxdxxxxdxxxdxxgxfV