Module 7part 1

Mathematics 31 - Module 7 Assignment Booklet 40 Section 2 Assignment: Areas Read all the parts of your assignment carefully and record your answers in the appropriate place. 1. Consider the region bounded above by f(x) = x, below by the x-axis, on the left by x = 0, and on the right by x = 5. The region has been divided into five vertical strips (as shown in the diagram). 4 a. Approximate the area of each strip using an inscribed rectangle, and find the sum of the areas of those rectangles. How is that sum related to the exact area? Draw a diagram to support your answers. Mathematics 31 - Module 7 Assignment Booklet 4 b. Approximate the area of each strip using a circumscribed rectangle, and find the sum of the areas of those rectangles. How is that sum related to the exact area? Draw a diagram to support your answers. 4 c. If n inscribed rectangles were used, what would the expression be, in sigma (E) notation, that approximates the exact area? How is the value of this approximation related to the exact area if n approaches infinity? Mathematics 31 - Module 7 Assignment Booklet 2 d. Write the definite integral representing the exact area, and evaluate that integral. 2. Evaluate the following integrals. Give the exact value. 3 a. [ 2x+1 dx