Area as a Function Consider the function . (a) Use NINT on

Chapter 10, Problem 10.1.1.312

(choose chapter or problem)

Area as a Function Consider the function \(f(t)=3 t^{2}\).

(a) Use NINT on a calculator to compute \(A(x)\) where A is the area under the graph of ƒ from \(t=0 \text { to } t=x \text { for } x=0.25\), 0.5, 1, 1.5, 2, 2.5, and 3.

(b) Make a table of pairs \((x, A(x))\) for the values of x given in part (a) and plot them using graph paper. Connect the plotted points with a smooth curve.

(c) Use a cubic regression equation to model the data in part (b) and overlay its graph on a scatter plot of the data.

(d) Make a conjecture about the exact value of \(A(x)\) for any x greater than zero.

(e) Find the derivative of the \(A(x)\) found in part (d). Record any observations.

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