Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1

We actually have to graph first the equation to see the extent of the curve. This is because we only have the distance formula to calculate the linear distance between two points. So, if the curve between x=0 and x=1, is more of a curve, then we cannot use the distance formula. However, looking at the graph, we can see that it is nearly linear. Therefore, our approximation using the distance formula can be valid. The distance formula is

d = √(x₂-x₁)²+(y₂-y₁)²

At x=0, the corresponding y=3. Similarly, when x=1, y=4. Using these coordinates and the formula,

d = √(1-0)²+(4-3)²
d = √2 = 1.4 units

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