Further Maths - Integrating and Differentiating Inverse Trig Functions

See Also

• [[Further Maths - Mean Value of a Function]]^S
• [[Further Maths - Improper Integrals]]^S
• [[Further Maths - Hyperbolic Functions]]^S

Flashcards

$$\frac{d}{dx}(\sin^{-1}(x))$$ What is this equal to??

$$ \frac{1}{\sqrt{1 - x^2}} $$

$$\frac{d}{dx}(\cos^{-1}(x))$$ What is this equal to??

$$ -\frac{1}{\sqrt{1 - x^2}} $$

$$\frac{d}{dx}(\tan^{-1}(x))$$ What is this equal to??

$$ \frac{1}{1 + x^2} $$

$$\int \frac{1}{\sqrt{1-x^2}} dx$$ What is this equal to??

$$ \sin^{-1}(x) + c $$

$$\int -\frac{1}{\sqrt{1-x^2}} dx$$ What is this equal to??

$$ \cos^{-1}(x) + c $$

$$\int \frac{1}{1 + x^2}dx$$ What is this equal to??

$$ \tan^{-1}(x) + c $$

$$\int \frac{1}{\sqrt{a^2-x^2}} dx$$ What is this equal to??

$$ \sin^{-1}\left(\frac{x}{a}\right) + c $$

$$\int \frac{1}{a^2 + x^2}dx$$ What is this equal to??

$$ \frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right) + c $$

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Backlinks

• [[Maths - Integration by Parts]]^S
• [[Further Maths - Syllabus]]^S

Metadata

date: 2021-04-29 15:50
tags:
- '@?further-maths'
- '@?public'
- '@?school'
- '@?methods-in-calculus'
title: Further Maths - Integrating and Differentiating Inverse Trig Functions