Let f be a function that is twice differentiable for all real numbers. The table above gives selected values for f" in the closed interval 2 <= x <= 12. Use a right Riemann sum with the four subintervals indicated by the data in the table to approximate int_2^(12) f'(x)dx. Show the work that leads to your answer.

Urijah Zhang

Urijah Zhang

Answered question

2022-11-29

x 2 4 8 9 12 f ( x ) 4 1 2 0 3
Let f be a function that is twice differentiable for all real numbers. The table above gives selected values for f" in the closed interval 2 x 12. Use a right Riemann sum with the four subintervals indicated by the data in the table to approximate 2 12 f ( x ) d x. Show the work that leads to your answer.

Answer & Explanation

jordipedretr39

jordipedretr39

Beginner2022-11-30Added 5 answers

We have n=4, i.e [ 2 , 4 ] , [ 4 , 8 ] , [ 8 , 9 ] , [ 9 , 12 ]
So, 2 12 f ( x ) d x using right Riemann sum
= ( 4 2 ) [ f ( 4 ) ] + ( 8 4 ) [ f ( 8 ) ] + ( 9 8 ) [ f ( 9 ) ] + ( 12 9 ) [ f ( 12 ) ] = 2 ( 1 ) + 4 ( 2 ) + 1 ( 0 ) + 3 ( 3 ) = 2 8 + 0 + 9 = 3

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