b The following expression represenls lhe integral/- f(:|:]dz {or some real number a and b. and a func1ion f. 8 lim sin(2 + 3) Question 10 a} Find A: and mi in lhis expression and deduce ll1e values old and b, and the function f. The A: len'n should be an expression involving 11., Ii should he an expression involving 1he index i and n. a and b are real numbers, and z) should be an expression involving 2. Don't forget to include square brackets; use calculator nolnlion [e.g. 3:2 is written 3 a 2"2]; and list your answers separated by commas. Answer: [A1, Zia\": b,f[z)] = E] 3 h} Compule the value ofthe lirnit above. Give your answer lo four decimal places. 11 . 4 4' Answer: 11m sin 2+i = Number nmoi=1n n Question 11 Compute the integral / f(x)dr, where the graph of f is the red curve given in the following figure. Note: On the graph of f , all points that are relevant for this computation have integer coordinates; the blue line is just for reference and is not the r-axis. 6 5- 4 2 1 2 6 8 X Answer: texas - FORMATTING: Give an exact answer. In Mobius, * is written pi.Question 12 The goal of this exercise is to approximate the value of the definite integral _ (x- 1)da using a Riemann sum with left endpoints and 8 subintervals (i.e. using the Riemann sum Lg)- a) If you sub-divide the interval 5, 7) into 8 subintervals of equal length Ar, you get 8 subintervals of the form [I;_1, I;] whose union is the interval [5, 7]. Find the endpoints *0, $1, . .., Ig that define these 8 subintervals FORMATTING: To enter your answer, list the endpoints in the form [TO, $1, . .., Ig] including the square brackets [ ] and a comma (,) between endpoints. The endpoints should be exact numbers, ordered from left to right. Answer: [x0, $1, . . .,28] = b) Compute the exact value of each term ; = f(I;_])Ax of the Riemann sum Lg- FORMATTING: To enter your answer, list the terms in the form [t1, to,. . ., tg] including the square brackets [ ] and a comma () between consecutive terms. Each term must be an exact number. Answer: [1,t2, . . .,t;] = c) Compute the value of the Riemann sum Lg. Write your answer with an accuracy of two decimal places. Answer: Number- Question 13 Suppose that f is a function which is integrable on the entire real line, and that a and 6 are real numbers. Which of the following statements are true? Check each one that is true. O Sandx = (6- a) for any real number n. O If f(x)