Calculus Questions 1 and 2

1. [-/25 Points] DETAILS SCALCET8 5.1.AE.001. MY NOTES PRACTICE ANOTHER EXAMPLE 1 Use rectangles to a y = 2x2 from 0 to 1 (the lustrated to the left). SOLUTION We first notice that the area must be somewhere between 0 and 2 because S is contained in a rectangle of side lengths 1 and 2, but we can certainly do better than that. Suppose we divide the region into four strips by drawing vertical lines x = 1, x = }, and x = 3, as in the Figure (a) below y = 2x y =2x Video Example 10 $3 We can approximate each strip by a rectangle whose base is the same as the strip and whose height is the same as the right edge of the strip (as in Figure (b) above). In other words, the heights of these rectangles are the values of the function f(x) = 2x2 at the right endpoints of the subintervals , ]. 4 2]. 2 4). and 4. 1]. Each rectangle has width * and the heights are 2(4)", 2()", 2()", and 2(1)2. If we let Re be the sum of the areas of these approximationg rectangles, we get RX - 4.2(4)' + 4.2(2)' +4.2(2)? + 4 .2(1)2 We see that the area A is less than R4 , So A