Question 2 The definition of the definite integral is: fe f (x) da = lim n E f(a;) Ax n - 00 i =1 A computer was used to calculate several Riemann Sums for the function f(x) on the interval [0, 2]. (We don't have the formula for f (x) in this problem.) The results are shown in this table. Riemann Sums E f(a;) Ax i =1 100 5.2536 10,000 5.33253336 1,000,000 5.33332533334 Recall that a limit is a trend. Also note that 10 = 5.3 This table is showing that the limit (or trend) of the Riemann Sums is , as n grows large. We write the previous statement using limit notation like this: lim 1 - 00 i =1 Question: what shall we conclude about the definite integral? A Warning: This problem checks a common misconception! You might want to discuss this problem before selecting your answer. Of f(x) de = 16Question 5 Let g(a) be the function graphed here. What would the definite integral for g (x) da measure? O The absolute value of the area bounded by y = g (x ) and the x-axis on the interval [0, 6]. O The net signed area bounded by y = g (@ ) and the x-axis on the interval [0, 0]. The positive area bounded by y = g (x) and the x-axis on the interval [0, 6].Question 3 Which of the following is equal to So g (x) da? O -1 . fig (x) da O Question 4 Recall that a definite integral equals a net signed area. Recall that regions above the x-axis contribute positive value, and regions below the x-axis contribute negative value. Question: For which of these intervals [a,b] is the definite integral ( sin a da equal to zero? Use a graph of y = sin a to decide. You could graph here, or at desmos.com e To create the graph, you can type y=sin x. To change the scale of the horizontal axis, you can select the wrench symbol. For horizontal axis step-size of 7, you can type pi. Q