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Trigonometric Substitution

Which trigonometric substitution is typically used for integrals involving $\sqrt{a^2-x^2b^2}?$

$x=\frac{a}{b}\tan\ \tan\ u$

$x=\frac{a}{b}\sin\sin u$

$x=\frac{a}{b}\sec\sec u$

When using the tangent substitution, what trigonometric identity is often applied to simplify the integral?

Pythagorean identity Double

angle identity Power

reduction identity

What is the integral of cosh cosh x dx?

Sinh sinh x + C

tanh tanh x + C

x+C

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2b^2-a^2}$ ?

$x=\frac{a}{b}\tan\tan u$

$x=\frac{a}{b}\sin\sin u$

$x=\frac{a}{b}\sec\sec u$

What is the purpose of trigonometric substitution in calculus?

To simplify complex trigonometric expressions

To evaluate integrals involving trigonometric functions

To solve trigonometric equations

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2-a^2}$ when x > a?

Cosine substitution

Tangent substitution

Secant substitution

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2b^2+a^2}$

$x=\frac{a}{b}\tan\tan u$

$x=\frac{a}{b}\sin\sin u$

$x=\frac{a}{b}\sec\sec u$

What is the integral of $\sec\sec xdx?$

$\ln\ln\left|\sec\sec x-\tan\tan x\right|+c$

$\ln\left|\sec\sec x\right|+C$

$\ln\ln\left|\sec\sec x+\tan\tan x\right|+C$

Which trigonometric substitution is typically used for integrals involving $\sqrt{a^2-x^2}?$

Secant substitution

Tangent substitution

Sine substitutio

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2+a^2}$ when x>a ?

Cosine substitution

Tangent substitution

Secant substitution

Questions

Time

Score

Trigonometric Substitution

Which trigonometric substitution is typically used for integrals involving ﻿a2−x2b2?\sqrt{a^2-x^2b^2}?a2−x2b2​?﻿

﻿x=abtan⁡ tan⁡ ux=\frac{a}{b}\tan\ \tan\ ux=ba​tan tan u﻿

﻿x=absin⁡sin⁡ux=\frac{a}{b}\sin\sin ux=ba​sinsinu﻿

﻿x=absec⁡sec⁡ux=\frac{a}{b}\sec\sec ux=ba​secsecu﻿

When using the tangent substitution, what trigonometric identity is often applied to simplify the integral?

Pythagorean identity Double

angle identity Power

reduction identity

What is the integral of cosh cosh x dx?

Sinh sinh x + C

tanh tanh x + C

x+C

Which trigonometric substitution is typically used for integrals involving ﻿x2b2−a2\sqrt{x^2b^2-a^2}x2b2−a2​﻿ ?

﻿x=abtan⁡tan⁡ux=\frac{a}{b}\tan\tan ux=ba​tantanu﻿

﻿x=absin⁡sin⁡ux=\frac{a}{b}\sin\sin ux=ba​sinsinu﻿

﻿x=absec⁡sec⁡ux=\frac{a}{b}\sec\sec ux=ba​secsecu﻿

What is the purpose of trigonometric substitution in calculus?

To simplify complex trigonometric expressions

To evaluate integrals involving trigonometric functions

To solve trigonometric equations

Which trigonometric substitution is typically used for integrals involving ﻿x2−a2\sqrt{x^2-a^2}x2−a2​﻿ when x > a?

Cosine substitution

Tangent substitution

Secant substitution

Which trigonometric substitution is typically used for integrals involving ﻿x2b2+a2\sqrt{x^2b^2+a^2}x2b2+a2​﻿

﻿x=abtan⁡tan⁡ux=\frac{a}{b}\tan\tan ux=ba​tantanu﻿

﻿x=absin⁡sin⁡ux=\frac{a}{b}\sin\sin ux=ba​sinsinu﻿

﻿x=absec⁡sec⁡ux=\frac{a}{b}\sec\sec ux=ba​secsecu﻿

What is the integral of﻿sec⁡sec⁡xdx?\sec\sec xdx?secsecxdx?﻿

﻿ln⁡ln⁡∣sec⁡sec⁡x−tan⁡tan⁡x∣+c\ln\ln\left|\sec\sec x-\tan\tan x\right|+clnln∣secsecx−tantanx∣+c﻿

﻿ln⁡∣sec⁡sec⁡x∣+C\ln\left|\sec\sec x\right|+Cln∣secsecx∣+C﻿

﻿ln⁡ln⁡∣sec⁡sec⁡x+tan⁡tan⁡x∣+C\ln\ln\left|\sec\sec x+\tan\tan x\right|+Clnln∣secsecx+tantanx∣+C﻿

Which trigonometric substitution is typically used for integrals involving ﻿a2−x2?\sqrt{a^2-x^2}?a2−x2​?﻿

Secant substitution

Tangent substitution

Sine substitutio

Which trigonometric substitution is typically used for integrals involving ﻿x2+a2\sqrt{x^2+a^2}x2+a2​﻿ when x>a ?

Cosine substitution

Tangent substitution

Secant substitution

Incorrect

Great!

Which trigonometric substitution is typically used for integrals involving $\sqrt{a^2-x^2b^2}?$

$x=\frac{a}{b}\tan\ \tan\ u$

$x=\frac{a}{b}\sin\sin u$

$x=\frac{a}{b}\sec\sec u$

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2b^2-a^2}$ ?

$x=\frac{a}{b}\tan\tan u$

$x=\frac{a}{b}\sin\sin u$

$x=\frac{a}{b}\sec\sec u$

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2-a^2}$ when x > a?

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2b^2+a^2}$

$x=\frac{a}{b}\tan\tan u$

$x=\frac{a}{b}\sin\sin u$

$x=\frac{a}{b}\sec\sec u$

What is the integral of $\sec\sec xdx?$

$\ln\ln\left|\sec\sec x-\tan\tan x\right|+c$

$\ln\left|\sec\sec x\right|+C$

$\ln\ln\left|\sec\sec x+\tan\tan x\right|+C$

Which trigonometric substitution is typically used for integrals involving $\sqrt{a^2-x^2}?$

Which trigonometric substitution is typically used for integrals involving $\sqrt{x^2+a^2}$ when x>a ?