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. . ———————————————————————————————————– 1.  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.  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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