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# Exam_exam_1_ - MIDTERM 1 MATH 141 FALL 2009 BOYLE Use...

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MIDTERM 1 — MATH 141 — FALL 2009 — BOYLE Use exactly ONE answer sheet per question (use the back of the sheet if needed). Put your name, your TA’s name and the question number on EACH page. Put a BOX around the ﬁnal answer to a question. No books. No notes. No calculators, cell phones or other electronic devices. Show enough work that we can follow your thinking. Simplify answers. It suﬃces to copy the pledge on your ﬁrst answer sheet, which we interpret to apply to all. Possible points are in square brackets, e.g. [20]. ———————————————————————————————————– 1. [20] Let R be the region between the x -axis and the graph of y = x ( x 3 + 1) 1 / 4 over the interval [0 , 2]. What is the volume V of the solid of revolution formed by rotating R around the x -axis? 2. [20] Find the center of gravity ( x, y ) of the semicircular region consisting of the points ( x,y ) such that x 2 + y 2
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