C2 : The Trapezium Rule Learning Objective : To learn a numerical method for evaluating integrals

Example Find the area under the curve y = √ 5x − x 2 for values of x between 0 and 4.

ABCD For greater accuracy, we can use a greater number of trapezia.

Trapezium rule for n strips of width h: A ≈ ½ x h x [ y 0 + y n + 2 (y 1 + y 2 + … + y n-1 ) ]A ≈ ½ x strip width x [ ends + twice middles ] If we have n strips, we have n + 1 ordinates. The strips must be evenly spaced

Example 1 Use the trapezium rule with six strips to find an approximation to ∫ x 2 dx Give your answer correct to 4 sig fig Area = square units (4 sf)

Example 2 Use the trapezium rule with five ordinates to find an approximation to ∫ √ 1 + x 2 Give your answer correct to 4 decimal places Area = 4·5098 (4 dp)