Exercises for Question Type 1: Evaluating definite integrals analytically

Question 1

Skill question

Evaluate the definite integral

$\int_{0}^{1} 3 x^{2} d x$

[2]

Question 2

Skill question

Find the value of the integral

$\int_{0}^{3} x 9 - x^{2} d x$

[5]

Question 3

Skill question

Find

$\int_{0}^{\frac{π}{4}} tan (x) d x$

[3]

Question 4

Skill question

Evaluate

$\int_{0}^{(\frac{π}{2})^{1/3}} 9 x^{2} cos (x^{3}) d x$

[6]

Question 5

Skill question

This question assesses the ability to evaluate a definite integral of the reciprocal function using the natural logarithm and the Fundamental Theorem of Calculus.

Evaluate the integral

$\int_{1}^{e} \frac{1}{x} d x$

[2]

Question 6

Skill question

Compute

$\int_{0}^{1} 2 x (1 + x^{2})^{3} d x$

[4]

Question 7

Skill question

Find the value of

$\int_{0}^{1} ln (1 + x) d x$

[6]

Question 8

Skill question

Calculate the value of

$\int_{0}^{\frac{π}{2}} cos^{2} (x) d x$

[3 marks]

[3]

Question 9

Skill question

This question requires the use of substitution to evaluate a definite integral involving an exponential function.

Evaluate $\int_{0}^{1} x e^{x^{2}} d x$

[4]

Question 10

Skill question

Compute

$\int_{0}^{2} 2 x d x$

[3]

Question 11

Skill question

Evaluation of a definite integral using the power rule.

Evaluate

$\int_{1}^{2} \frac{1}{x ^{2}} d x$

[3]

Question 12

Skill question

Find the value of

$\int_{0}^{\frac{π}{2}} sin (x) d x$

[3]

IB Mathematics Applications & Interpretation Question Type 1: Evaluating Definite Integrals Analytically Exercises