Let g(x)= 2x +3. Let A(t) denote the area of the region bounded by g above, the x-axis below, the y- axis to the left, and the vertical line x=t on the right. (We consider only t0) Find and expression for A(t) and graph this function on the interval [0,3]

Question

Let g(x)= 2x +3. Let A(t) denote the area of the region bounded by g above, the x-axis below, the y- axis to the left, and the vertical line x=t on the right. (We consider only t>0) Find and expression for A(t) and graph this function on the interval [0,3]

anonymous · Answer

Hint: You will have 4 graphs, inequalities, as follows, (1) g(x) = y ≤ 2x +3; 
(2) x-axis, y ≥ 0; (3) y – axis, x ≥ 0; and (4) x ≤ 3. The intersection of these graphs will be a trapezoid, so we look at the formula of the area of a trapezoid:

A = (1/2)h(b1 + b2) → A(t) = (1/2) t∙[g(0) + g(t)].

anonymous · Answer

another hint:
1. g(x) is a straight line so, give it a shot.
2. axis boundaries are given too..
3. as soon as you draw your g(x), the answer will show up