3. Trigonometric Integrals and Trigonometric Substitution

Root Expressions And Trig Substitution — Quiz

Test your understanding of root expressions and trig substitution with 5 practice questions.

Practice Questions

Question 1

Which trig substitution matches the standard form $\sqrt{a^2-x^2}$ if you want to use $1-\sin^2\theta=\cos^2\theta$?

Question 2

Which trig substitution matches the standard form $\sqrt{a^2+x^2}$ if you want to use $1+\tan^2\theta=\sec^2\theta$?

Question 3

Which trig substitution matches the standard form $\sqrt{x^2-a^2}$ if you want to use $\sec^2\theta-1=\tan^2\theta$?

Question 4

If $x=3\sin\theta$, what is $dx$?

Question 5

If $x=4\tan\theta$, what does $16+x^2$ become after substitution?