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4.2 The Definite Integral: Problem 7 Previous Problem Problem List Next Problem (1 point) 17 -10 f(a)da- f(x) dx = / f(x) dx 6 6 a where ( and b(1 point) Definition. The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximationg rectangles A = lim R,, = lim f(x1)Ar + f(32)Ar + . .. + f(In) Ax. (a) Use the above definition to determine which of the following expressions represents the area under the graph of f (x) = 3 from a = 0tor = 1 A. lim 11-00 n B. lim c. lim 1=1 D. lim (# ) 1=1 (b) Evaluate the limit that is the correct answer to part (a), You may find the following formula for the sum of cubes helpful: 72 13+2+3 + -- - +n 123 n(n + 1) 2 2 The value of the limit is(1 point) Let f" () =3+214/8 (a) Find the most general formula for f(r ), It an arbitrary constant must be used here, use an upper case "(" (b) Based on your answer to (a), find the most general formula for / ( ) . If another new arbitrary constant must be used here, use an upper case "D" f(x) = Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining Email instructor(1 point) Consider the function f (x) = Let F(x) be the antiderivative of f ( ) with F(1) = 0. Then F(x) = Preview My Answers Submit Answers You have attempted this problem 2 times Your overall recorded score is 0% You have unlimited attempts remaining Email instructor(1 point) Use six rectangles to find an estimate of each type for the area under the given graph of f from x = 0to r = 12. -1 13 1. Take the sample points from the left-endpoints Answer: L6 = 2. Is your estimate Le an underestimate or overestimate of the true area? Choose one 3. Take the sample points from the right-endpoints Answer: Rs = 4. Is your estimate Is an underestimate or overestimate of the true area? Choose one 5. Take the sample points from the midpoints. Answer Me =4.2 The Definite Integral: Problem 1 Previous Problem Problem List Next Problem (1 point) The following sum 3 1 09 + 3 100 + + ...+ 1+ 1 + + 1+ 3n n is a right Riemann sum for a certain definite integral .b f(x) dx using a partition of the interval [1, b] into 72 subintervals of equal length. Then the upper limit of integration must be: b = and the integrand must be the function f (x) = Note: You can earn partial credit on this