Calculus II - Arc Length (Practice Problems)

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Section 8.1 : Arc Length

Set up, but do not evaluate, an integral for the length of y=√x+2 , 1≤x≤7 using,
1. $\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx$
2. $\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy$
Solution
Set up, but do not evaluate, an integral for the length of x=cos(y) , 0≤x≤12 using,
1. $\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx$
2. $\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy$
Solution
Determine the length of $y = 7{\left( {6 + x} \right)^{\frac{3}{2}}}$ , $189 \le y \le 875$ . Solution
Determine the length of $x = 4{\left( {3 + y} \right)^2}$ , $1 \le y \le 4$ . Solution