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Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 8.2 : Surface Area
- Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating \(y = 7x + 2\) , \( - 5 \le y \le 0\) about the \(x\)-axis using,
- \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
- \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
- Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating \(y = 1 + 2{x^5}\) , \(0 \le x \le 1\) about the \(x\)-axis using,
- \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
- \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
- Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating \(x = {{\bf{e}}^{2y}}\) , \( - 1 \le y \le 0\) about the \(y\)-axis using,
- \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
- \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
- Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating \(y = \cos \left( {\displaystyle \frac{1}{2}x} \right)\) , \(0 \le x \le \pi \) about
- the \(x\)-axis
- the \(y\)-axis
- Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating \(x = \sqrt {3 + 7y} \) , \(0 \le y \le 1\) about
- the \(x\)-axis
- the \(y\)-axis
- Find the surface area of the object obtained by rotating \(\displaystyle y = \frac{1}{4}\sqrt {6x + 2} \) , \(\displaystyle \frac{{\sqrt 2 }}{2} \le y \le \frac{{\sqrt 5 }}{2}\) about the \(x\)-axis.
- Find the surface area of the object obtained by rotating \(y = 4 - x\) , \(1 \le x \le 6\) about the \(y\)-axis.
- Find the surface area of the object obtained by rotating \(x = 2y + 5\) , \( - 1 \le x \le 2\) about the \(y\)-axis.
- Find the surface area of the object obtained by rotating \(x = 1 - {y^2}\) , \(0 \le y \le 3\) about the \(x\)-axis.
- Find the surface area of the object obtained by rotating \(x = {{\bf{e}}^{2y}}\) , \( - 1 \le y \le 0\) about the \(y\)-axis.
- Find for the surface area of the object obtained by rotating \(y = \cos \left( {\displaystyle \frac{1}{2}x} \right)\) , \(0 \le x \le \pi \) about the \(x\)-axis.