Exercises for Question Type 2: Trigonometric substitution in integrals - IB | RevisionDojo

IB
Question Type 2: Trigonometric substitution in integrals

Question Type 2: Trigonometric substitution in integrals Exercises

Question 1

Find

\int \frac{x^2}{\sqrt{4 - x^2}}\,\mathrm{d}x

Question 2

Find $\int \frac{x^3}{\sqrt{4 - x^2}}\,dx$

[5]

Question 3

Find $\int \sqrt{x^2 + 9}\,dx$

[7]

Question 4

Evaluate

\int \sqrt{4 - x^2}\,dx

[6]

Question 5

Find

\int \sqrt{x^2 - 9}\,dx

[6]

Question 6

Evaluate

\int \frac{x^2}{\sqrt{x^2 - 9}}\,dx

[7]

Question 7

Compute

\int \frac{x^3}{(x^2 + 4)^{\frac32}}\,dx

[6]

Question 8

Evaluate

\int \frac{x}{\sqrt{4 - x^2}}\,dx

[5]

Question 9

Find

\int \frac{dx}{x\sqrt{x^2 + 4}}

[6]