EduNinja

[Maximum number: 8]

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

f(x)=\frac{-x^{2}}{50}+2 x+30, \text { for } 0 \leq x \leq 70

(a)

Write down the integral which can be used to find the area of the shaded region R.

[ 4 ]

$\quad \int_{0}^{70} \frac{-x^{2}}{50}+2 x+30 \mathrm{~d} x \quad$ A1A1

Note: Award A1 for a correct integral, A1 for correct limits in the correct location. Award at most A0A1 if d x is omitted.

(b)

Find the area of Linda's field.

Linda used the trapezoidal rule with ten intervals to estimate the area. This calculation underestimated the area by $11.4 \mathrm{~m}^{2}$ .

[ 4 ]

( Area $=) 4710 \mathrm{~m}^{2}\left(4713.33 \ldots, \frac{14140}{3}\right) \quad$ A2

IB Maths AI HL Sl 5 5 Integration As Anti Differentiation Topic Practice

Learn this topic

IB Maths AI HL Sl 5 5 Integration As Anti Differentiation Topic Practice

Learn this topic

Question 1

Question (a)

Question (b)