Question

Approximate the area of the region bounded by the graph of f(t) f(t) cos(t/2-7t / 8) (t/2-7T/8) and the cos t-axis on [7T/8,15/ 8] with n 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle (see figure) 0.5 27 2 The approximate area of the region is (Round to two decimal places as needed.) N| a.

Answer 1

This problem is based on approximating area under given graph using mid point rule

7IT ft1-Cos Given 5 IT 7T DD b=S1T a= 11 given that Now So ISIT-TIT 6-9 n UST 4- 4 T 4 poin ts are t 8 So Sample 13 IT 1S IT tu Fnow that formula foy we NOW mid Point ue fs given AH Fho

At 2 A4 above fomula becomes ffi-1tti My= 2 f +f(zt ty)1 2 NOw Put q the valves

11 IT +A/111 T 91T -l My 2 13T SIT 4 2 My-frtm)+ f()+ 위 프)+f(팩]] 끝 S11 Mu +CoS 2 31T 70 Cos 2 Mu=(0.30268 34 22 tWto. 923819522 1 )T7y 2.36 6 930 68-2.31 My area ob the rejon appooximate Ts 2-37 AuA