These extra practice problems are for students who wish to have an extra set to practice. These problems do not have a posted solution so students should reflect on ways to determine whether their answer is correct. Feel free to discuss with peers to solve these problems.

Use the trapezoid rule and Simpson’s 1/3 or 3/8 rules to integrate the following data. Compare the answers.

x

y

0

4

0.5

4.958851

1

5.682942

1.5

5.99499

2

5.818595

2.5

5.196944

3

4.28224

3.5

3.298434

4

2.486395

4.5

2.04494

5

2.082151

5.5

2.588919

6

3.441169

6.5

4.43024

7

5.313973

7.5

5.876

8

5.978716

8.5

5.596974

9

4.824237

9.5

3.849698

10

2.911958

Use all three Newton-Coates methods to determine the answer to the following integral. Break the integral into as many parts as you prefer. Compare the answers.

$$\int_0^{10}\frac{3x^2}{1-2x}dx$$

Use the Romberg method to solve the following equation.

$$\int_1^{4}\frac{\sin z+2x}{z^2}dz$$

Use Gauss Quadrature’s 2PT, 3PT, and 4PT methods to solve the following equation.

$$\int_0^{5}\frac{\cos x\sin^2x}{x-6}dz$$