Question

Use the Midpoint Rule with n=4 to approximate the following integral, where x is measured in radians. So sin(x) dx You must show all steps of your work. Please express all intermediate steps to six decimal places or more, and then round your final answer to 4 decimal places. (Do not round off to four decimal places until you get to your final answer.) CAUTION: Make sure that your calculator is in RADIANS mode! 17.4286 17.2183 16.7873 16.7629 15.9287

Answer 1

The answer is given as

Solo ор By using Mid-point rule, with n = 4 we have to find approximate value of the integral joo sinux du 4 Now 80 let I So sin se da The width of the sub-interval h = 80- O 2o 4 and the sub- interval will be- [0, 20], [20,40], [40, 60], [60,80]

and so 30 Now mid-point og each interval 0, 50, 70 respect actively By Mid-point will BO So Sindre da h [sindio + Sinu30 + Sin/50 + sin 870 -80 sina da u 20 [sindło + sinuso + sin 850 + sinto 20[-0.020 20683 + (-0.72 1495)+(0.708861) + (0.87 1463)] n 20 [-0.742178 + 1.58034 ~ 20 (0.838146) 80 Sin e da SS 16.76292

hence, the 9 approximate Value given integral by Mid-point the of rule is So 80 sina da 5 16.7629