第5章 5.23

r=aθ(a>0)(r,θ)r = a\theta \qquad (a > 0) \qquad (r, \theta)

s=∫0θa2θ2+a2 dθ=a[12{θθ2+1+log⁡∣θ+θ2+1∣}]0θs = \int_0^\theta \sqrt{a^2\theta^2 + a^2}\, d\theta = a\left[\frac{1}{2}\left\{\theta\sqrt{\theta^2+1} + \log\left|\theta + \sqrt{\theta^2+1}\right|\right\}\right]_0^\theta

=a2{θθ2+1+log⁡∣θ+θ2+1∣}= \frac{a}{2}\left\{\theta\sqrt{\theta^2+1} + \log\left|\theta + \sqrt{\theta^2+1}\right|\right\}

解説: r31bn1z