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Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. f(x) = 16-x2; [- 1,9] . . . . . The area between the x-axis and f(x) is. (Simplify your answer. Type an integer or an improper fraction.)\fAssume f(x) is continuous for g x s c as shown in the figure to the right. Write an equation relating the three quantities below. a b y = Xx) . . . . . Choose the correct answer below. a O B . Six)dx = [rexjax + freddx c b o c . Six jax = fixjax . frexlax a a C b a\fDiscuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample. b If Jx) dx = 0, then f(x) = 0 for all x in [a,b]. Select the correct answer below. a b O A. The statement is always true because Ix) dx = 0 and Ix) dx = 0 a b 1 O B. The statement is false. I x3 dx = 0 and x3 at 0 for all x in [ab]. -1 b O C- The statement is always true because I0 dx = 0. 1 O D. The statement is false. I x2 dx = 0 and x2 5* 0 for all x in [a,b]. -1 Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 50 _ (-31+ 4) i = 1 . . . . . Find the first three terms and the last term. 50 Z (-31+ 4) = (1 + + + ...+ i = 1 Find the sum of the sequence. 50 Z (-3i + 4) = 0 i = 1dy Find the particular solution for the differential equation = at y(0) = 4. dx 9y Choose the correct answer below. 1 4 OA. y X + 16 9 O B. y2 = 9x3 + 16 O C. y= 9x5 + 4 O D. y= 14+4