The continuous curve C has equation y=f(x). A table of values of x and y for y=f(x) is shown below.x4.04.24.44.6y=f(x)0y=f(x)1yy=f(x)3y=f(x)4y=f(x)5y=f(x)6y=f(x)7y=f(x)8Use the trapezium rule with all the values of y in the table to find an approximation forx0giving your answer to x1 decimal places.
Q. The continuous curve C has equation y=f(x). A table of values of x and y for y=f(x) is shown below.x4.04.24.44.6y=f(x)0y=f(x)1yy=f(x)3y=f(x)4y=f(x)5y=f(x)6y=f(x)7y=f(x)8Use the trapezium rule with all the values of y in the table to find an approximation forx0giving your answer to x1 decimal places.
Identify width of trapezium: Identify the width of each trapezium h. Since the x-values increase by 0.2, h=0.2.
Apply trapezium rule: Apply the trapezium rule: ∫f(x)dx≈(2h)×(y0+2y1+2y2+2y3+2y4+y5), where y0 to y5 are the y-values from the table.
Substitute values into formula: Substitute the values into the trapezium rule formula: 20.2 * 9.2+2×8.4556+2×3.8512+2×5.0342+2×7.8297+8.6.
Calculate sum inside parentheses: Calculate the sum inside the parentheses: 9.2+2×8.4556+2×3.8512+2×5.0342+2×7.8297+8.6=9.2+16.9112+7.7024+10.0684+15.6594+8.6.
Add up values: Add up the values: 9.2+16.9112+7.7024+10.0684+15.6594+8.6=68.1414.
Multiply sum by factor: Multiply the sum by (h/2): (0.2/2)×68.1414=0.1×68.1414.
Calculate final result: Calculate the final result: 0.1×68.1414=6.81414.
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