Mathematics

Mathematics

Problem

Let x=sin⁡tx=\sin t and y=cos⁡t+ty=\cos t + t for 0≤t≤π0\le t \le \pi. Which integral represents the arc length of this curve on the given interval? a) ∫0π(cos⁡t)2+(sin⁡t+1)2 dt\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2}+(\sin t + 1)^{2}}\,dt b) ∫0π(cos⁡t)2+(−sin⁡t+1)2 dt\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2}+(-\sin t + 1)^{2}}\,dt c) ∫0π(cos⁡t)2+(−sin⁡t)2 dt\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2}+(-\sin t)^{2}}\,dt d) ∫0π(cos⁡t)2+(cos⁡t+t)2 dt\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2} + (\cos t + t)^{2}}\,dt

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