Find the arc length of \(y=3x+1\) from \(x=0\) to \(x=2\).

Find the arc length of \(y=\frac{2}{3}x^{3/2}\) from \(x=0\) to \(x=3\).

Find the arc length of \(x=y^2/2\) from \(y=0\) to \(y=2\).

Find the arc length of \(y=\ln(\cos x)\) from \(x=0\) to \(x=\pi/4\).

Find the arc length of \(y=\cosh x\) from \(x=0\) to \(x=1\).

Find the arc length of the upper semicircle \(y=\sqrt{9-x^2}\) from \(x=-3\) to \(x=3\).

Find the exact arc length of \(y=x^2\) from \(x=0\) to \(x=1\).

A parametric curve is defined by \(x=t^2\) and \(y=t^3\) for \(0 \le t \le 1\). Find its arc length.

Set up, but do not evaluate, the integral for the arc length of \(y=e^{-x^2}\) from \(x=0\) to \(x=2\).

A learner finds the arc length of \(y=2x\) from \(x=0\) to \(x=5\) by computing \(\int_0^5(1+2^2)\,dx=25\). Explain the error and find the correct arc length.