IB Maths AI HL 5.8 Trapezoidal rule Question Bank

Linda owns a field, represented by the shaded region R. The plan view of the field is shown in the following diagram, where both axes represent distance and are measured in metres.

The segments [AB], [CD] and [AD] respectively represent the western, eastern and southern boundaries of the field. The function, f(x), models the northern boundary of the field between points B and C and is given by

Suggest how Linda might be able to reduce the error whilst still using the trapezoidal rule.

Linda would like to construct a building on her field. The square foundation of the building, EFGH , will be located such that $[\mathrm{EH}]$ is on the southern boundary and point F is on the northern boundary of the property. A possible location of the foundation of the building is shown in the following diagram.

The area of the square foundation will be largest when $[\mathrm{GH}]$ lies on $[\mathrm{CD}]$.