# Sketch the region bounded by the graphs of y = 2 x and y =...

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Math 172 Written Assignment 1 Name: ID#: Lab Section#: 1. Integrate. Simplify answers. a) integraldisplay e 4 r +8 dr b) integraldisplay π π/ 2 sin(3 x ) dx c) integraldisplay 2 + 3 x 5 x dx d) integraldisplay 4 3 t radicalbig 100 - 4 t 2 dt
2. Sketch the region bounded by the graphs of y = 2 x and y = 7 x - x 2 and find its area. Find the points of intersection algebraically (not by guessing and checking). 3. The region between y = cos( x ) and y = cos(2 x ) for 0 x π is shown below. Find the total area of this region. You’ll need to find the x -value c ; you may use a guess-and-check approach. 4. Sketch the region bounded by the graphs of y = 6 - 1 2 x and x = 2 y 2 , and find its area. Find the points of intersection algebraically (not by guessing and checking).
5. Use the slicing method to find the volume of the solid whose base is the region bounded by the semicircle y = 1 - x 2 and the x -axis, and whose cross sections through the solid perpendicular to