Area? ?functions?? ?L?et A(?x) ?be the area of the region bounded by the t-axis and the graph?of ? y = f(?t) ? om t = 0 ?to t = x. Consider the following functions and graphs. a.? Find A(2) ? b.? Find A? (6) c.? Fin?d?a formula for ?A(x ? ) (see figure)

Step-by-step solution Step 1 o f 10 Consider is the area of the region bounded by the axis and the graph of from and Step 2 o f 10 The given graph is shown below: Step 3 o f 10 (a) To Find : The value of the is the area of the shaded region between the graph of and axis from . Step 4 o f 10 The graph of the region is shown below: Step 5 o f 10 Hence the required area equal to the area of the triangle whose base is in the interval . Remember the area of a triangle is: base x height Area of triangle = 2 Using the formula for area of the triangle,