Solve both 32 and 33 please 32) Let R be the region bounded by the graphs of f(x) = sin(x) and g(x) = x and the1. Let T be the solid obtained by rotating R around thelines x = -1 and x =у-ахis.a) The volume of T is given by 2n S-1 x(x – sin(x))dx.b) The volume of T is given by 47 S x(x – sin(x))dx.c) The volume of T is given by 4T S, x(x – sin(x))dx.d) The volume of T is given by 27 S', x|(x – sin(x))|dx.--e) None of the above.33) The diagram below contains the graph of f(x) = sin(x) on the interval [0, 7] andthe line y = ¿.1/2n/2Which of the following statements are true?a) The average value of the function f(x) = sin(x) on the interval [0, 7] is less thanb) The average value of the function f(x) = sin(x) on the interval [0, 7] is .c) The average value of the function f(x) = sin(x) on the interval [0, 7] is greaterthan .d) Suppose that N is an unknown integer. | sin(N)| is likely closer to 1 than it isto 0.e) Suppose that N is an unknown integer. sin(N) | is likely closer to 0 than it isto 1.

(32) Height of the shell (h) = x-sin(x) Radius of the shell = x We know,V = ∫ab2πshell radius(shell…

32) Let R be the region bounded by the graphs of f(x) = sin(x) and g(x) = x and the lines x = -1 and x = 1. Let T be the solid obtained by rotating R around the y-axis. a) The volume of T is given by 27 S', ¤(x – sin(x))dx. b) The volume of T is given by 4n f ¤(x – sin(x))dx. c) The volume of T is given by 4T S', ¤(x – sin(x))dx. d) The volume of T is given by 27 S, ¤|(x – sin(x))|dx. e) None of the above. 33) The diagram below contains the graph of f(x) = sin(x) on the interval [0, 7] and the line y = . 1/2- a/2 Which of the following statements are true? a) The average value of the function f(x) = sin(x) on the interval [0, 7] is less than %3D b) The average value of the function f(x) = sin(x) on the interval [0, r] is §. c) The average value of the function f(x) = sin(x) on the interval [0, r] is greater than . d) Suppose that N is an unknown integer. | sin(N)| is likely closer to 1 than it is to 0. e) Suppose that N is an unknown integer. | sin(N)| is likely closer to 0 than it is to 1.