Question

of your choice. Draw a graph of fx) Problem: Apply various integration techniques to compute Note the labsolute values!. Take f(0) to be: 2n divided by 6. 1. Obtain Trapezoidal estimate with one panel, Ti. Copy it in the table below. 2. Obtain Trapezoidal estimate with two panels, T. Copy it in the table. 3. Obtain Trapezoidal estimate with four panels, Ta. Copy it in the table. 4. Obtain Trapezoidal estimate with eight panels, Ts. Copy it in the table. Complete the Romberg Table belowusing o decimalsinour answers: Ti empty box R33 R43 T2 R22 R32 R42 empty box R44 T& 5. Explain in one or two lines, why the error in the final entry Ras is O(h) 6. How many panels are needed for the composite trapezoidal method to guarantee an accuracy of 10+? For simplicity, assume that the second derivative of f(x) is 6. Show all relevant computations below: Answer: N= 7. Use Gaussian quadrature with n-5 to compute this integral. The weights (coefficients) are given in our book. Show steps below. If needed, use the back of this sheet. Answer with 6 decimals

Answer 1

イ(n) 0 hure h

3/h 49,9 at. Γι.oug',2- 3 3 IS LK 63