Question

9. Determine the area of the region bounded by the graph of f(x) = sinº(5x) cos(5x) and the x-axis between x = -0.2262 and x = 0.2953, giving your answer to 4 decimals. A) 0.0584 B) 0.0634 C) 0.0684 D) 0.0734 E) 0.0784

Answer 1

f(u) sin" (5x) cos(51 The area of the region bounded by f(n) and az - 0.2262 and X= 0.2953 is given by, 0.2953 R-anis in between area s $(w) dre 9 - 0.22 62 We first derive the integral. I s from de "(5x) C03 ( 5x) dhe s sint 2 S sin(su) sin (54) cos (54) de 3 sin (5) Z +/ sin (154) sin(su) cos(su) dom 3 sind ( sin 30 - 4 sino) $ [ 3.sin(sw) - sin (way) sin (rou) da N (: "2 sino coso = sin 20

11 3 8 sin (su) sin(10 m)du - $ f sin (154) in (10%) dhe is [cos (5m) – cos (15m)]bke to [ cos (su) (su) – cos ( 25 »)] cm 2 N 16 Cos (50) du 3 16 To COS (154) dm + To se CO3 (259) dm sin (15 oc) Sin (56) 40 + sin (250) 400 80 So, from equation (1) 0.2953 sin (54) sin (154) 80 sin (252) area + 40 400 -0.2262 0.03919 +.0.02426| (in in Radian mode) 0.06 338 F 0.0634 Cortion (B))
At the last step, while evaluating the values of sin(cx), where c is a constant, we have to put the value of cx in radian.