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Let y=g(x) be the particular solution to the differential equation {d y}/{d x}=g'(x) with initial condition g(2)=7. Selected values of g' are given in the table above. The function g is three-times differentiable.
(c) Use a right Riemann sum with the two subintervals indicated by the data in the table to approximate ∫₂²² g'(x)dx. Show the computations that lead to your answer.
(d) It is known that g''(x)<0 for 2 ≤x ≤ 2.2 . Is the approximation from part (c) an overestimate or an underestimate for ∫₂²² g'(x)dx ? Give a reason for your answer
Let y=g(x) be the particular solution to the differential equation {d y}/{d x}=g'(x) with initial condition g(2)=7 Selected values of g' are given in the table above. The function g is three-times differentiable.
(e) Use the approximation for ∫₂²² g'(x)dx from part (c) to estimate the value of }g(2.2) . Show the computations that lead to your answer.
