Alice Starts at the Origin and Walks Along the Graph $y=\frac{x^{2}}{2}$

question 1

Multiple Choice

Alice starts at the origin and walks along the graph of $y=\frac{x^{2}}{2}$ at a velocity of 6 units/second.Which of the following integrals show how far Alice has traveled when she reaches the point where x = a?

• A) \(\int_{0}^{a \sqrt{6}} \sqrt{1+x^{2}} d x\)
• B) \(\int_{0}^{a} \sqrt{1+x^{2}} d x\)
• C) \(\int_{0}^{6 a} \sqrt{1+x^{2}} d x\)
• D) \(6 \int_{0}^{a} \sqrt{1+x^{2}} d x\)

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