5.2 Worksheet #5 (Volumes Using Washers)

5.2 Worksheet #5 (Volumes Using Washers)

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Fill in the Blanks

 Let f and g be the functions given by $f\left(x\right)=1+\sin\left(2x\right)$   and $g\left(x\right)=e^{\frac{x}{2}}$ . Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. Find the volume of the solid generated when R is revolved about the x-axis. 

(PLEASE ROUND TO 3 DECIMAL PLACES)

If you didn't get the correct answer be sure to figure out your mistake before moving onto the next question.

Fill in the Blanks

Let R be the region bounded by the y-axis and the graphs of  $y=\frac{x^3}{1+x^2}$  and $y=4-2x$  . Find the volume of the solid generated when R is revolved around the x-axis.

(PLEASE ROUND TO 3 DECIMAL PLACES)

If you didn't get the correct answer be sure to figure out your mistake before moving onto the next question.

Fill in the Blanks

Let R be the region in the first quadrant bounded by the graph of  $y=2\sqrt{x}$ , the horizontal line  $y=6$ , and the y-axis.  Find the volume of the solid generated when R is revolved around the horizontal line  $y=7$ .  

(PLEASE ROUND TO 3 DECIMAL PLACES)

If you didn't get the correct answer be sure to figure out your mistake before moving onto the next question.

Fill in the Blanks

Let R be the region bounded by the graph of $y=\ln x$ and the line  $y=x-2$ .  Find the volume of the solid generated when R is revolved around the line  $y=-3$ .   

(PLEASE ROUND TO 3 DECIMAL PLACES)

If you didn't get the correct answer be sure to figure out your mistake before moving onto the next question.

Fill in the Blanks

Let R be the region bounded by the graph of $y=\ln x$ and the line  $y=x-2$ .  Find the volume of the solid generated when R is revolved around the line  $x=-1$ .   

(PLEASE ROUND TO 3 DECIMAL PLACES)

If you didn't get the correct answer be sure to figure out your mistake before moving onto the next question.

Fill in the Blanks

Let R be the region bounded by the graphs of $y=\sqrt{x}$ ,  $y=e^{-3x}$ , and the vertical line  $x=1$ .  Find the volume of the solid generated when R is revolved about the horizontal line  $y=1$ .

(PLEASE ROUND TO 3 DECIMAL PLACES)