Exercises for Question Type 2: Integrals for total area (using absolute value)

Question 1

Skill question

Find the total area between the curve $y = x^{3} - x^{2} - 32 x + 60$ and the $x$ -axis on $[- 6, 5]$ .

[8]

Question 2

Skill question

Find the total area enclosed by the curve $y = x^{2} - 4 x$ and the x-axis for $0 \leq x \leq 5$ .

[6]

Question 3

Skill question

Find the total area between the curve $y = x^{3} - x$ and the x-axis on $[- 2, 2]$ .

[5]

Question 4

Skill question

Calculate the total area between the curve $y = x^{3}$ and the x-axis over $[- 2, 2]$ .

[4]

Question 5

Skill question

Determine the total area between $y = cos x$ and the $x$ -axis on $[- \frac{π}{2}, \frac{3 π}{2}]$ . [5 marks]

[5]

Question 6

Skill question

Compute the total area between the curve $y = x^{2} - x - 6$ and the x-axis on $[- 2, 4]$ .

[7]

Question 7

Skill question

Find the total area between the curve $y = x^{2} - 9$ and the x-axis on the interval $[1, 4]$ .

[6]

Question 8

Skill question

Find the total area between $y = x^{3} - 6 x$ and the x-axis on $[- 3, 3]$ .

[6]

Question 9

Skill question

Find the total area between the curve $y = x^{2} - 4$ and the x-axis on the interval $[- 3, 3]$ .

[5]

Question 10

Skill question

Determine the total area enclosed by $y = sin (2 x)$ and the x-axis on $[0, π]$ .

[5]

Question 11

Skill question

Compute the total area between $y = x^{4} - 4 x^{2}$ and the $x$ -axis on $[- 3, 3]$ .

[6]

Question 12

Skill question

Calculate the total area enclosed by $y = sin x$ and the x-axis on $[0, 2 π]$ .

[5]

IB Mathematics Analysis and Approaches Question Type 2: Integrals for Total Area Exercises