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Integration — WMA12 IAL Mathematics practice questions · Study-IAL

Subjects
Mathematics
WMA12
2.8

Integration

WMA12Topic 2.83 questions

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Definite integrals, areas under curves and the trapezium rule.

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Questions

Multiple choice: 1
Calculation: 2
Total: 3

Previous topic2.7Differentiation

Sample questions

Original practice questions written in the style of the exam.

Question 16 marks
The curve $C$ has equation $y = 6x - x^2$ and the line $l$ has equation $y = 2x$ .

Find the exact area of the finite region bounded by $C$ and $l$ .
Mark scheme
- M1 Sets $6x - x^2 = 2x$ (1)
- A1 $x = 0$ and $x = 4$ (1)
Question 24 marks
Use the trapezium rule with 4 strips of equal width to estimate $\displaystyle\int_0^2 \sqrt{1 + x^3}\,dx$ , giving your answer to 3 decimal places.

x=

4

M1 Integrates the difference,

\int (4x - x^2)\,dx

, or curve minus triangle (1)

A1

2x^2 - \dfrac{x^3}{3}

(1)

M1 Applies limits 0 and 4 (1)

A1 Area

= \dfrac{32}{3}

(1)

d

x

Mark scheme

B1 Strip width $h = 0.5$ (1)
B1 $y$ values $1,\ 1.0607,\ 1.4142,\ 2.0917,\ 3$ (1)
M1 Uses $\tfrac{h}{2}\left[y_0 + y_4 + 2(y_1 + y_2 + y_3)\right]$ (1)
A1 $3.283$ (1)

y4

+

2

(

y1

+

y2

+

y3

)

]