Calculate the exact length of the curve on the interval .

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

Problem

Calculate the exact length of the curve y=x22y=\dfrac{x^{2}}{2} on the interval [−1,1][-1,1]. (a) 222\sqrt{2} (b) 2+2ln⁡(1+2)\sqrt{2}+2\ln\bigl(1+\sqrt{2}\bigr) (c) 2+ln⁡(1+2)\sqrt{2}+\ln\bigl(1+\sqrt{2}\bigr) (d) ln⁡(1+2)\ln\bigl(1+\sqrt{2}\bigr)

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