Arc length practice problems
The length of a curve: ∫ √(1 + (dy/dx)²) dx. 15 problems with worked solutions; in 15 of them every equation is proved by a computer algebra system.
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 2 \) to \( \displaystyle x = 7 \).
Find the length of the curve \( \displaystyle y = \frac{x^{4}}{8} + \frac{1}{4 x^{2}} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 3 \).
Find the length of the curve \( \displaystyle y = \frac{x^{4}}{8} + \frac{1}{4 x^{2}} \) from \( \displaystyle x = 2 \) to \( \displaystyle x = 3 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 2 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 4 \).
Find the length of the curve \( \displaystyle y = \frac{x^{4}}{8} + \frac{1}{4 x^{2}} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 2 \).
Find the length of the curve \( \displaystyle y = \frac{x^{4}}{8} + \frac{1}{4 x^{2}} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 4 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 3\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 2 \) to \( \displaystyle x = 3 \).
Find the length of the curve \( \displaystyle y = \frac{2 x^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 6 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 3\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 2 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 2 \) to \( \displaystyle x = 9 \).
Find the length of the curve \( \displaystyle y = \frac{2 x^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 2 \) to \( \displaystyle x = 4 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 3\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 3 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 3\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 1 \) to \( \displaystyle x = 4 \).
Find the length of the curve \( \displaystyle y = \frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3} \) from \( \displaystyle x = 0 \) to \( \displaystyle x = 7 \).