Math 191Practice Prelim 1Fall 2005No calculators, notes or books allowed.To improve the chance for partial credit and also generally ease the work of grading,please:•write clearly and be well organized;•use the page backs for ungraded scrap work and for checking your answers;•box inyour answers; and•reduce your answers as much as possible.None of the calculations are longandnone of the answers are long.1. Evaluate the following expressions:a)integraldisplaysec2(x)dxb)ddtintegraldisplay1t3cos4(x)dxc)integraldisplay2-2x31 +x6dx2. Consider the region bounded on the left by they-axis and on the right by thecurvesy= sin(x) andy= cos(x). Find the area of the region.3. a) Express the area under the curvey= sin(x) betweenx= 0 andx=π6as alimit of Riemann sums. (Use uniform partitions and the right hand rule.)
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Riemann, Right-hand rule, sin B sin, cos B sin