1. In Topic 4.2 (The Definite Integral II), we considered f(x)=19-x on [-3, 3] We know that the function produces a semi-circle and the definite integral gives the area between the curve and the x-axis. [, 9-x3 dx =_ 1(3) = Due to symmetry, we know that the bottom half of this circle has the same area as the top, so we can double our previous result to find the area of a whole circle with radius 3 units. 9 A =2 -1 Now think about this function on [0, 3]. We know the area given by 1 9-x' dx = 2, How can we use this information and an understanding of symmetry to find the area given by [, vo - x' dx Can we generalize this to situations beyond circles? Give an example (even if you don't know how to compute a particular area yet). 2. Let f (x) = e* on [0, 4] You will soon be able to compute AVG[0,4] = 13.4 Sketch the function and a geometric interpretation of the average-value given. Use words to describe the inherent geometry in this example