Question

Let

f(x) = 14 − 2x.

(a)

Sketch the region R under the graph of f on the interval

[0, 7].

The x y-coordinate plane is given. There is 1 line and a shaded region on the graph.

• The line enters the window at y = 13 on the positive y-axis, goes down and right, and exits the window at x = 6.5 on the positive x-axis.
• The region is below the line.

The x y-coordinate plane is given. There is 1 line and a shaded region on the graph.

• The line enters the window at y = 14 on the positive y-axis, goes down and right, and exits the window at x = 7 on the positive x-axis.
• The region is below the line.

The x y-coordinate plane is given. There is 1 line and a shaded region on the graph.

• The line enters the window at the origin, goes up and right, and ends at the point (7, 14).
• The region is below the line.

The x y-coordinate plane is given. There is 1 line and a shaded region on the graph.

• The line enters the window at y = 14.5 on the positive y-axis, goes down and right, and ends at the point (7, 0.5).
• The region is below the line.

Find its exact area (in square units) using geometry.

49  square units

(b)

Use a Riemann sum with five subintervals of equal length

(n = 5)

to approximate the area (in square units) of R. Choose the representative points to be the right endpoints of the subintervals.

  square units

(c)

Repeat part (b) with ten subintervals of equal length

(n = 10).

  square units

(d)

Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger n?

Yes/No   

Answer 1