Applications of Integration practice questions

Secondary 4 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise applications of integration free

What this topic covers

Area Between a Line and a Curve
Area Bounded by a Curve and the x-axis
Definite Integrals
Properties of Definite Integrals

Worked examples

Example 1

Evaluate

\displaystyle\int_{0}^{2} (12x^{3} + 6x^{2}) \, dx

Show the worked solution

$\int_{0}^{2} (12x^{3} + 6x^{2}) \, dx = \left[\frac{12}{4}x^{4} + \frac{6}{3}x^{3}\right]_{0}^{2}$
$= \left[3x^{4} + 2x^{3}\right]_{0}^{2}$
$= 3(2)^{4} + 2(2)^{3}$
$$= 48 + 16$$
$$= 64$$

Answer: $64$

Example 2

Given that

\displaystyle\int_{2}^{7} f(x) \, dx = 6

, evaluate

\displaystyle\int_{2}^{7} [2f(x) + 2] \, dx

Show the worked solution

$\int_{2}^{7} [2f(x) + 2] \, dx = 2\int_{2}^{7} f(x) \, dx + \int_{2}^{7} 2 \, dx$
$= 2 \times 6 + 2(7 - 2)$
$$= 12 + 10$$
$$= 22$$

Answer: $22$

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.