Exercises for Question Type 1: Applying integration through using the basis integrals

Question 1

Skill question

Evaluate the definite integral $\int_{0}^{\frac{π}{4}} cos (4 x) d x$ .

[4]

Question 2

Skill question

Find the indefinite integral $\int sin (x) d x$ .

[1]

Question 3

Skill question

Find the indefinite integral $\int sin (5 x) d x$ .

[3]

Question 4

Skill question

Compute the indefinite integral $\int (5 cos (x) - 7 sin (x) + \frac{4}{x}) d x$ .

[4]

Question 5

Skill question

Compute the indefinite integral $\int (6 sin (3 x) - 9 cos (3 x)) d x$ .

[4]

Question 6

Skill question

Evaluate the definite integral $\int_{0}^{\frac{π}{2}} (2 sin x + 3 cos x) d x$ .

[3]

Question 7

Skill question

Compute the indefinite integral $\int (10 sin (x) - \frac{2}{x} + 5 cos (x)) d x$ .

[4]

Question 8

Skill question

Find the indefinite integral $\int (3 sin (2 x) - 4 cos (2 x)) d x$ .

[3]

Question 9

Skill question

Evaluate the indefinite integral $\int (3 sin (x) + cos (x) - \frac{2}{x}) d x$ .

[4]

Question 10

Skill question

Find the indefinite integral $\int (3 cos (2 x) + \frac{1}{x} - 2 sin (2 x)) d x$ .

[5]

Question 11

Skill question

Evaluate the definite integral $\int_{1}^{e} (sin (x) + \frac{1}{x}) d x$ .

[4]

Question 12

Skill question

Evaluate the definite integral $\int_{1}^{2} (2 cos (x) - \frac{1}{x}) d x$ .

[4]

IB Mathematics Analysis and Approaches Question Type 1: Applying Integration Through Using the Basis Integrals Exercises