My Notes EXAMPLE 1 Use rectangles to estimate the area under the parabola y = 4x2 from 0 to 1 (the parabolic region S illustrated to the left) 1.4) SOLUTION We first notice that the area must be somewhere between and 4 because S is contained in a rectangle of side lengths 1 and 4, but we can certainly do better than that. Suppose we divide the region into four strips by drawing vertical lines x =-x =-, and x =-as in the Figure (a) below Video Example S2 Ss 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 functionæx) = 4x2 at the right endpoints of the subintervals 10 4 2 ( 4ã 4( -, and 4(1)2. If we let R4 be the sum of the Each rectangle has width A and the heights are 4 areas of these approximating rectangles, we get