Calculate the arc length of the parabola from to .

MATHEMATICS · Single correct · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

Calculate the arc length of the parabola y=12x2y=\dfrac{1}{2}x^{2} from x=0x=0 to x=1x=1. (a) 12(2+ln⁡(2))\dfrac{1}{2}\bigl(\sqrt{2}+\ln(\sqrt{2})\bigr) (b) 12(2+ln⁡(1+2))\dfrac{1}{2}\bigl(\sqrt{2}+\ln(1+\sqrt{2})\bigr) (c) 2+ln⁡(1+2)\sqrt{2}+\ln(1+\sqrt{2}) (d) 23(22−1)\dfrac{2}{3}\bigl(2\sqrt{2}-1\bigr)

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