Explain the answer please

(13m 1223) SULIT CONFIDENTLAL QUESTION 4 (25 MARKS) Consider the autonomous differential equation with the initial condition gash}, y(0)=0_1, IE[D,0.15], m=oms a) Find the Euler's approximation. [Express all calculations in 5 decimal points.] [6 marks] b) Find the 4th-Order Runge-Kutta's approximation. [Express all calculations in 5 decimal points] [1 1 marks] c) Using the solutions from part a) and b), find the comparison with the exact solution to determine the absolute errors. [8 marks] QUESTION 3 (25 MARKS) Given the following integral, with its exact integral is 0.8939 b) 1.3 I 5x 9'\" dx 0 1 Find your answer by using a Simpson's U3 rule with step size is 0.6 to estimate its inteng function. Then, determine its absolute error. [Round-up all the calculations to 4 decimal points] [12 marks] Estimate its integral function by using the three-segment trapezoidal rule. Then, nd its absolute error. [Round-up all the calculations to 4 decimal points] [12 marks] From part a) and b), identify which method is better to estimate its integral function? [1 mark]