1. Calculate the area of the region in the first quadrant bounded by the curve y = x^3 and the line y = a x where a = 1.xxxx is a decimal number (xxxx represent the last four digits of your student id number)

    First do the calculation by integration. Then use numerical integration using Riemann sums method, trapezoid method and Simpsons' method. Compare the methods by finding the number of subdivisions necessary to get the result to agree with the exact solution in first six decimal places. Send me the result obtained by integration, and the results of numerical calculations by each method (with the numbers of subdivisions involved). Include the programs you used.

  2. Write a program which calculates the area in the first problem using the Monte Carlo method.

  3. Calculate the area of the region in the first quadrant bounded by the y-axis, the curve y = cos(x) and y = 2 a x where a = 0.xxxx is a decimal number (xxxx represent the last four digits of your student id number).

    Use any method we discussed in class. Describe in detail the procedure you used to find the answer, enclose the programs and the final result.

E-mail your solutions to milicic@math.utah.edu. This assignment is due April 14th.