a) Calculate 2 dx x using trapezoidal rule with 5 intervals (Assume 1 is not known) 1 b) Suppose that you know = ln x + c Calculate the area under the curve. c) Calculate the percentage Solution y0 =1.0000 y0 = 1.0000 y1 = 0.8333 2y1 = 1.6666 y2 = 0.7143 2y2 = 1.4286 y3 = 0.6250 2y3 = 1.2500 y4 = 0.5556 2y4 = 1.1112 y5 =0.5000 y5 = 0.5000 Total Sum = 6.9564  0.2 2 1 5 = 120 2 h  2 2 2 2 2 Then =      y1 y2 y3 y4 y5 xdx 0.2 6.9564 = 2 1 = 10 x6.9564 = 0.69564 = 0.6956 to four decimals. b) Now, 1 2
a) Calculate 2 x dx using trapezoidal rule with 5 intervals (Assume 1 is not known) b) Suppose that you know 1 = ln x + c Calculate the area under the curve. c) Calculate the percentage Solution y0 =1.0000 y0 = 1.0000 y1 = 0.8333 2y1 = 1.6666 y2 = 0.7143 2y2 = 1.4286 y3 = 0.6250 2y3 = 1.2500 y4 = 0.5556 2y4 = 1.1112 y5 =0.5000 y5 = 0.5000 Total Sum = 6.9564 = 2 1 5  0.2 120 Then 2 xdx = h  2 y1  2 y2  2 y3  2 y4  2 y5  = 0.2 2 6.9564 = 1 10 x6.9564 = 0.69564 = 0.6956 to four decimals. b) Now, 2 1
CALCULUS%20II.DOCX