1. Evaluate the following integral S² a. Analytically b. Numerically using: -20 20x7 + 5x5 + 15x³ + 20x dx i. ii. A single application of trapezoidal rule. Composite trapezoidal rule with n=4. Composite Simpsons' 1/3 rule with n=4 iv. Multiple Simpsons' rules with n=5 iii. Compute the true error for all the numerical estimates using the analytical value evaluated in part a.

How large should n be to guarantee that the Trapezoidal Rule approximation to - 2 (- a4 12a 48x2 + 2x + 5) dx is accurate to within 0.1. 4 n = How large should n be to guarantee that the Simpsons Rule approximation to | (- x4 – 12x – 48x? + 2x + 5) dx is accurate to within 0.1. -4 n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n

Solve the question in the same way as a book and the Q is complete

8. What is the minimum value of y = -3 sin x + 5? (K) а. -8 b. 2 C. -2 d. 8