Cross-Sectional Volume (AP Calculus)

Find the area of the region enclosed by the lines and curves y=x, y=0, y= $\frac{1}{x^2}$  , x=2.  

•  $\frac{3}{2}$  

•  $1$  

•  $\frac{2}{3}$  

•  $\frac{6}{5}$  

Find the area of the region enclosed by the lines and curves y=x+1 and  $y=3-x^2$  

•  $\frac{9}{2}$  

•  $\frac{13}{2}$  

•  $\frac{5}{3}$  

•  $\frac{15}{4}$  

The base of a solid is the region enclosed between the graphs of y=sinx and y=-sinx from x=0 to x= $\pi$ . Each cross section perpendicular to the x-axis is a semicircle with diameter connecting the two graphs.  Find the volume of the solid. 

•  $\frac{\pi^2}{8}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi^2}{4}$  

•  $\frac{2\pi^2}{3}$  

Find the volume of the figure formed when a base, bounded by  $x=y^2$  and  $0\le x\le4$  , has cross-sections perpendicular to the x-axis that are squares.

• 30

•  $\frac{115}{4}$  

• 36

• 32

Find the volume of the figure formed when the region bounded by  $y=e^x$  for  $1\le y\le5$  has cross-sections perpendicular to y that are rectangles, with a height 3 times that of the base. (Calculator active)

• .133

• ,891

• 14.571

• ,283

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