Exercises for Question Type 5: Area between two curves with changing dominance

Question 1

Skill question

Specification

Compute the area between the curves $y = sin x$ and $y = cos x$ for $0 \leq x \leq π$ .

[5]

Question 2

Skill question

Determine the area enclosed between $y = x^{3}$ and $y = 2 x$ on $- 2 \leq x \leq 2$ .

[7]

Question 3

Skill question

Determine the area between $y = 4 x - x^{2}$ and $y = x$ for $0 \leq x \leq 4$ .

[8]

Question 4

Skill question

Determine the area between $y = x^{2} - 4$ and $y = 2 x - 4$ for $0 \leq x \leq 4$ .

[7]

Question 5

Skill question

Compute the area enclosed between $y = cos x$ and $y = sin x$ for $0 \leq x \leq \frac{π}{2}$ .

[6]

Question 6

Skill question

Find the area enclosed between the curve $y = x^{3} - x$ and the $x$ -axis for $- 1 \leq x \leq 1$ .

[6]

Question 7

Skill question

Find the area between the curves $y = x^{2}$ and $y = 4 - x$ for $0 \leq x \leq 4$ .

[6]

Question 8

Skill question

Calculate the area between the curves $y = x^{3} - x^{2} - x$ and $y = x$ over $- 1 \leq x \leq 2$ .

[7]

Question 9

Skill question

Calculate the area between the curves $y = x^{2}$ and $y = x$ for $0 \leq x \leq 2$ .

[6]

Question 10

Skill question

Find the area between the curves $y = x^{2} - 2 x$ and $y = 2 - x^{2}$ for $0 \leq x \leq 3$ .

[7]

Question 11

Skill question

Compute the area between $y = x^{2}$ and $y = 4 - x^{2}$ for $- 3 \leq x \leq 3$ .

[7]

Question 12

Skill question

Find the area between the curves $y = 3 x - x^{2}$ and $y = x^{2} - x$ over $0 \leq x \leq 3$ .

[7]

IB Mathematics Analysis and Approaches Question Type 5: Area Between Two Curves with Changing Dominance Exercises

Specification