Use the indicated methods to solve the following problems with nonuniform grids The function f is twice differentiable on ( , ) Values of f at various points on 0, 20 are given in the table a Approximate in three ways using a left Riemann sum, a right Riemann sum, and the Trapezoid Rule b A scatterplot of the data in the table is provided in the figure Use the scatterplot to illustrate each of the approximations in part (a) by sketching appropriate rectangles for the Riemann sums and by sketching trapezoids for the Trapezoid Rule approximation c Evaluate 0 4 8 20 12 14 S(x) 3 4 2 1 20 f(x) dx Jo

Question: Use the indicated methods to solve the following problems with nonuniform grids. The function f is twice differentiable on (-, ). Values of f at

Use the indicated methods to solve the following problems with nonuniform grids.

The function f is twice differentiable on (-∞, ∞). Values of f at various points on [0, 20] are given in the table.

0 | 4 8 20 12 14 S(x) 3 4 -2 -1

a. Approximate 20 f(x) dx Jo in three ways: using a left Riemann sum, a right Riemann sum, and the Trapezoid Rule.

0 | 4 8 20 12 14 S(x) 3 4 -2 -1

b. A scatterplot of the data in the table is provided in the figure. Use the scatterplot to illustrate each of the approximations in part (a) by sketching appropriate rectangles for the Riemann sums and by sketching trapezoids for the Trapezoid Rule approximation.

c. Evaluate 20 f(x) dx Jo

0 | 4 8 20 12 14 S(x) 3 4 -2 -1 20 f(x) dx Jo

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