IB Maths AI HL Sl 5 5 Integration As Anti Differentiation Questions

Practise IB Mathematics SL/HL 5.5 by applying integration as anti-differentiation methods to questions from the Question Bank.

Exam points

Find polynomial-type antiderivatives and include the constant of integration.
Use a boundary condition to determine the constant and connect an antiderivative to a definite integral.
Calculate or interpret area under a curve, including bounds, units and sign.

[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.

Figure for Question IB Maths AI HL Sl 5 5 Integration As Anti Differentiation Questions question 1 — IB Maths AI HL

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

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IB Maths AI HL Sl 5 5 Integration As Anti Differentiation Questions question 1

Question (a)

Question (b)