Assignment:
Q1. Evaluate the improper integral:
Infinity
∫ (xe^x^2)dx
0
Q2. Complete the square, then use integration tables to evaluate the indefinite integral:
∫ {(sqrt(x^2 + 6x + 13))/x+3}dx
Q3. Which of the following would be used to find the present value of the income given by e(i)=4000e measured in dollars, over four years at an annual interest rate of 5%.
Q4. Integrate:
∫ (1/x^2-9)dx
Q5. A function f is given by the following table:
X 0 1 2 3 4
F(x) 9 8 7 9 2
Estimate the area between the x-axis and y=f(x) from x=0 to x=4 using Simpson’s Rule.
Q6. Use Simpson’s Rule with n=2 to approximate the value of ∫-12 (3/2x-1)dx
Provide complete and step by step solution for the question and show calculations and use formulas.