Please answer using pi as needed

5 Find the center of the mass of a thin plate of constant density o covering the region bounded by the x-axis and the curve y = , cos x, - - sxs?. The center of the mass is located at (x, y) = (0.] (Type an exact answer, using it as needed.) VI VI More View an example Get more help Q Search pause 19 f 10 f71 $12 O 3 5 P R Y U O W E S F G H K D V B N MDate Page Answer The coordinates of centre of mase is given by a dm M where ME total may y do: infinitesimal 1 fydm Small element M Let's calculate integrals to find centre of mass VM = dm ( d A X S ( - density 18 "constant Now, wing dA zy da = 5 coen an 17 72: NOW, M - J S ( os n d n = 58 2 5 8 sim ( 1 / 7 ) - 1 M = 2 realme Shot on realme 9i 5G 2023 07 14 21:08. . ". . . . . . . . . ." . . . . . . ." . . . .".". 144 .... .". . . .".". 2023 07 14 21:08 insert prt sc delete O backspace home Date - Pago_ Now, a -coordinate centre of mass Nov fordm M a S d A M M N f 2 coon an a sina + cosx) + c N & M By using ILATE guile furdv = u/ vdv - ( 4' vdu) du Now, applying limits N I sin It cos I - ( - I sin ( - AT ) + (us / - ) am - N T sinn toga 2 = 0 realme Shot on realme 91 5GPage Now, y - coordinate of centre of mass y = ] fydm M y x 5 corn In m 2 M 2 5 cosn ) ( 5 (osu ) dy 95 f cos 2 x doc um 2 ) 25 13 27 25 ( at sin zu ) + c 8 m Now apply limits 2 2 5 LT + Sin27 - 1 + Sim / = 25 ) 8 m 7 FAAAN 2 =1 25 2 7 + 8 sin 2 1 / 7 7 2 ) 25 2 I f sin ( 25 ] 8 M puting value in from ey - 1 - 1 25 5 21 + sin / 25 7 8 x 5 8 s in ( a ) 10 1 + 5 = ) 5 6 8 sim I ) 7 realme Shot on realme 9 5G 2023 07 14 21:08insert prt so delete O backspace home Date Now, centere of mass + 5 2 8 8 5 in I ) 8 8 2023 07 14 21:08 realme Shot on realme 9i 5G