Write as a Vector Equality y=x^3 , y=0 , x=1 , x=2

Problem

y=x3,y=0,x=1,x=2

Solution

1. Identify the components of the vector function. A vector equality for a curve in the plane is typically written in the form r*(t)=<x(t),y(t)>

2. Parameterize the independent variable. Let x=t

3. Substitute the parameter into the function. Since y=x3 then y=t3

4. Define the interval for the parameter. Based on the vertical lines x=1 and x=2 the parameter t must satisfy 1≤t≤2

5. Construct the vector equation by combining the components into a single vector expression.

Final Answer

r*(t)=<t,t3>,1≤t≤2

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